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Full text of "Opticks : or, A treatise of the reflections, refractions, inflections and colours of light"

^ 

^Vr 




THE LIBRARY 

OF 

THE UNIVERSITY 

OF CALIFORNIA 

LOS ANGELES 



GIFT 

Dr. K. R. Beigelman 



'•k. 



». 



oPTiCKs: 

O R, A 

TREATISE 

O F T H E 

Reflections, Refradiqns^ 

InfieBions and Colours 



O F 



LIGHT. 



ne Fourth Edition, correSied, 



By Sir ISAAC NEWTON, Knt. 



L O N D N: 

Printed for William Innys at the Wefl- 
End of St. Paul's, Mdccxxx. 



© 



837 

■ ^. 'it 





Advertifement L 

ART of the en- 
fui?ig Difeourfe a- 
bout hight ivas 
"Written at the De- 
fire of fame Gen- 
tlemen of the Royal -Society, in 
the Tear 1^7^, and then fent to 
their Seeretary, and read at their 
Meetings, and the refiivas add- 
ed about tivehe Tears after to 
complete, the Theory ; except the 
third Book, and the lafl Propo- 
fit ion of the Second, vjhich "were 
fince put together out of f car- 
ter d Papers, To a\:oid be- 
ing engaged in Difputes about 

A z thefe 



Advertifement. 

thefe Matters, I haw hitherto de- 
layed the printing, and jhould 
flill ha've delayed it, had not the 
Importunity of Friends prevailed 
upon me. If any other Papers 
nvrit on this SubjeB are got out 
of my Hands they are imperfeB, 
and ivere perhaps ^written before 
I had tried all the Experiments 
here fet do'von, and fully fatisfi- 
ed my felf about theLaivs of Re* 
fraBions and Compofttion of Co- 
lours. I have here publijUd "vjhat 
I think proper to eome abroad, 
mping that it may not be tran- 
Jlated into another hanguage 
mthout my Confem. 

The Crowns of Colours, ivhieh 
fometimes appear about the Sun 
and Moon, I ha'oe endea'voured 
to gi've an Account of) but for 

"want 



Advertifement. 

^o^ant of fufficient Obfer'vations 
leave that Matter to be farther 
examined. The Siibjeti of the 
Third Book I have alfo left im- 
perfeBy not having tried all the 
Experiments "which I intended 
ivhen Iivas about the fe Matters, 
nor repeated fome ofthofe ivhich 
I did try, until I had fatisfied 
my felf about all their Circum- 
fiances. To communicate vjhat 
I have tried, and leave the refl 
to others for farther Enquiry, 
is all my Defign in publijhing 
thefe Papers. 

IndLettervjrittento Tlfr.Leib- 
nitz in the Tear I (!) 7^, and pub- 
lijhed by Dr, Wallis, / mention d 
a Method by vohich I had found 
fome general Theorems about 
fquaring Curvilinear Figures, 

or 



Advertifement. 

or comparing them mth the Co- 
nic SeBions, or other the jimplefl 
Figures mth v)hich they may be 
compared. And fome Tears ago 
I lent out a Manuscript contain- 
ing fuch Theorems, and halving 
fince met mth fome Things copi- 
ed out of it, I have on this Occa- 
fion made it public k, prefixing to 
it ^//Introdudion, and Subjoin- 
ing a Scholium concerning that 
Method, And Ihavejoinedrnth 
it another fmall TraB concern- 
ing the Curvilinear Figures of 
the Second Kind, "which ivas alfo 
"written many Tears ago, and 
made knov)n to fome Friends, 
"who have folic it ed the making it 
publicL 

April r. T M 

1704. X. -L^« 




dvertifement 11. 

this Second Edition 
[hefeOpticks Iha've 
oMtted the Mathema- 
tical ^aBs publipd 
at the End of the former Edi- 
tion, as not belonging to the 
SiibjeB. And at the End of 
the Third Book I ha%w added 
fome Queflions. And to fiev) 
that I do not take Gratuity for 
an ejfential Property of Bodies, 
I have added one Queflion con- 
cerning its Caufe, chiifing to 
propofe it by "way of a Quefli- 
on, becaufe I am not yet fatif- 
fied about it for vjant of Expe- 
riments. 



^^- IN. 




Advertisement to this 
Fourth Edition. 

HIS neuo Edition of 
Sir Ifaac Newtonx 
Opticks is carefully 
printed frow> the Third 
Edition, as it vjas correBed by 
the Author s oivn Hand, and 
left before his Death with the 
Bookfeller, Since Sir Ifaac j* 
Lediones Opticas, which he 
public kly read in the Uni'verfity 
of Cambridge in the Tears 
l66^, 16^0, and 16'ji, are 
lately printed, it has been thought 
proper to make at the bottom of 
the Pages fencer al Citations from 
thence, where may be found the 
Demonfirations, which the Au- 
thor omitted in thefe Opticks. * 



C I] 




THE 

FIRST BOOK 



O F 



OPTICKS. 



PART I. 



", Y Delign in this Book is not to ex- 
plain the Properties of Light by Hy- 
pothefes, but to propofe and prove 
them by Reafon and Experiments : 
In order to which I ihall premife the 
following Definitions and Axioms. 




B 



DEFI- 



B 



O P T I C K S. 
DEFINITIONS. 

D E F I N. I. 

T the Rays of Light I under/land its leafi 
TartSy and thofe as well Siiccejive in the 
fame Lines, as Contemporary in feveral Lines. 
For it is manifeft that Light confifts of Parts, 
both Succeflive and Contemporary j becaufe in 
the fame place you may ftop that which comes 
one moment, and let pafs that which comes pre- 
fently after; and in the fame time you may 
Hop it in any one place, and let it pafs in any 
other. For that part of Light which is ftopp'd 
cannot be the fame with fhat which is let pafs. 
The leafl Light or part of Light, which may 
be flopp'd alone without the reft of the Light, 
or propagated alone, or do or fuffer any thing 
alone, which the reft of the Light doth not or 
fuifers not, I call a Ray of Light. 

D E F I N. IL 

Refrangibility of the Rays of Light, is their 
T>ifpofition to be refraBed or turned out of their 
Way in pafjing out of one tranfparent Body or 
Medium into another. And a greater or lefs Re- 
frangibility of Rays, is their Difpofition to be 
turned more or lefs out of their Way in like^ In- 
cidences on the fame Medium. Mathematicians 
ufually confider the Rays of Light to be Lines 
reaching from the luminous Body to the Body 
illuminated, and the refradiion of thofe Rays to 
be the bending or breaking of thofe lines in 

their 



BOOK! 3 

their pafling out of one Medium into another. 
And thus may Rays and Refradions be confi- 
dered, if Light be propagated in an inftanr. 
But by an Argument taken from the i^qua- 
tions of the times of the Eclipfes of Jupiter i 
BatelliteSy it feems that Light is propagated in 
time, fpending in its pafTage from the Sun to us 
about feven Minutes of time: And therefore I 
have chofen to define Rays and Pvcfradions in 
fuch general terms as may agree to Light in both 
cafes. 

D E F I N. in. 

Reflexibility of Rays^ is fbeir Difpojitic?! to be 
rejieSted or turned back into the fame Mediu?n jroni 
any other Medium upon whoje Surface they fall. 
And Rays are more or lefs refexible, which are 
turned back more or lefs eafly. As if Light pafs 
out of a Glafs into Air, and by being iiiclmed 
more and more to the common Surface of the 
Glafs and Air, begins at length to be totally re- 
fledled by that Surface ; thofe io:::^ of Rays 
which at like Incidences are refledted moft co- 
pioully, or by inclining the Rays begin fooneil 
to be totally refledted, are mofl reflexible. 

D E F I N. IV. 

I'he A?jgle of Licidence is that Angle, u-hick, 
the Line defcribed by the incident Ray contains with 
the Perpendicular to the refeSiing or refracting Sur-- 
face at the, Point of Incidence, 



p2 DEFIN, 



4 O P T I C K S. 

D E F I N. V. 

^ke Afigle of Reflexion or HefraBion^ is the 

Angle which the line defcribed by the i'-eJleBed or re- 

fraBed Ray coiitaineth with the Perpendicular to 

the refleBing or refraSiifig Surface at the Point of 

Incidence, 

D E F I N. VL 

'^he Sines of Incidence^ Reflexion^ and Refra- 
Bion, are the Si?ies of the Angles of Incidence, Re- 
fexion, and Refr/^Bio?!. 

D E F I N. VII. 

^hc Light ivhofe Rays are all alike Refran- 
gible^ I call Simple, Homogeneal and Similar ; 
and that whofe Rays are fome more Refrangible 
than others, I call Compound, Heterogeneal and 
Diffijnilar. The former Light I call Homoge- 
neal, not becaufe I would affirm it fo in all re- 
ipedts, but becaufe the Rays which agree in Re- 
frangibility, agree at leaft in all thofe their other 
Properties which I confider in the following 
Difcourfe, 

D E F I N. VIII. 

\the Colours of Homogeneal Lights, I call Pri~ 
wary, Ilofjiogeneal and Simple j ajid thofe of He- 
teroge??.eal Lights, Heterogeneal ajid Compound. For 
thefe are always compounded of the colours of 
Homogeneal Lights j as will appear in the fol- 
lowing Difcourfe. 



'O 



AXIOMS. 



B O O K I. 5 

A X I MS. 

A X. I. 

npHR Ajigks of RefexioJi and "Refracllon^ lit 
in one and the fame Flane with the A?igle of In- 
cidence. 

A X. II. 

'The Angle of Refexion is equal to the Angle of\ 
Incidence. 

AX. III. 

If the ref-aBed Ray be returned direclly back to 
the Poifit of Incidence^ itJJ:all be rfraBed into the 
Line before defcribed by the incident Ray. 

A X. IV. 

RefraBion out of the rarer Medium into the 
denfer, is made towards the Perpendicular ; that 
is, Jo that the A?igle of Refraclion be lefs than the 
Angle of Incidence. 

: A X. \. 

The Siiie of Incidence is either accurately or 
'very nearly in a green Ratio to the Sine of Re- 
fraBion. 

Whence if that Proportion be known in any 
one Inclination of the incident Ray, 'tis known 
in all the Inclinations, and thereby the Refra- 
iftion in all cafes of Incidence on the fame refra- 
<fting Body may be determined. Thus if the 

B 3 R'efra- 



6 O P T I C K S. 

Refradion be made out of Air into Water, the 
Sine of Incidence of the red Light is to the Sine 
of its Refracftion as 4 to 3 . If out of Air into Glafs, 
the Sines are as 17 to 11. In Light of other 
Colours the Sines have other Proportions: but 
the difference is fo little that it need feldom be 
coniidered. 

Suppofe therefore, that RS [ in Fig. i. ] repre- 
fents the Surface of ftagnating Water, and that C 
is the point of Incidence in which any Ray coming 
in the Air from A in the Line A C is refledled or 
refrad:ed, and I would know whither this Ray 
fhall go after Reflexion or Refraction: I ereA 
upon the Surface of the Water from the point 
of Incidence the Perpendicular CP and produce 
it downwards to Q^, and conclude by the firft 
Axiom, that the Ray after Reflexion and Re- 
fradiion, fliall be found fomewhere in the Plane 
of the Angle of Incidence ACP produced. I let 
fall therefore upon the Perpendicular C P jthe 
Sine of Incidence A D j and if the refiedted 
Ray be deflred, I produce AD to B fo that 
D B be equal to A D, and draw C B. For this 
Line C B fhall be the refiedted Ray j the Angle 
of Reflexion B C P and its Sine B D being e- 
qual to the Angle and Sine of Incidence, as they 
ought to be by the fecond Axiom, But if the 
refra(5led Ray be defired, I produce A D to H, 
fo that D H may be to A D as the Sine of Re- 
fradion to the Sine of Incidence, that is, (if the 
Light be red) as 3 to 4; and about the Center 
C and in the Plane A C P with the Radius CA 
defcribing a Circle ABE, I draw a parallel to the 
Perpendicular CPQ^, the Line HE cutting tl^e 

Circum- 



B O O K I. 7 

Circumference in E, and joining C E, this Line 
CE fhall be the Line of the refradied Ray., 
For if E F be let fiiU perpendicularly on the 
Line P Q^ this Line E F fliall be the Sine of Re- 
fra<flion of the Ray C E, the Angle of Refradion 
being E C Qj^ and this Sine E F is equal to D H, 
and confequently in Proportion to the Sine of 
Incidence AD as 3 to 4. 

In like manner, if there be a Prifm of Glafs 
(that is, a Glafs bounded with two Equal and 
Parallel Triangular ends, and three plain and 
well polifhed Sides, which meet in three Parallel 
Lines running from the three Angles of one 
end to the three Angles of the other end) and 
if the Refradion of the Light in pafTing crofs this 
Prifm be defired: Let ACB [inFig,2.] reprefent 
a Plane cutting this Prifm tranfverlly to its three 
Parallel lines or edges there where the Light 
pafleth through it, and let D E be the Ray in- 
cident upon the firft fide of the Prifm A C where 
the Light goes into the Glafs ; and by putting 
the Proportion of the Sine of Incidence to the 
Sine of Refradion as 1 7 to 11 find E F the firft 
refraded Ray. Then taking this Ray for the 
Incident Ray upon the fecond fide of the Glafs 
B C where the Light goes out, find the next 
refraded Ray EG by putting the Proportion 
of the Sine of Incidence to the Sine of Re- 
fradion as II to 17. For if the Sine of Inci- 
dence out of Air into Glafs be to the Sine of 
Refradion as 17 to 11, the Sine of Incidence out 
of Glafs into Air muil on the contrary be to the 
Sine of Refradipn as 11 to 15^ by the third; 
A?«tom» 



S O P T I C K S. 

Much after the fame manner, if A C B D [in 
Fig. 2'] reprefent a Glafs fpherically convex on 
both fides (ufually called aLem^ fuch as is a Burn- 
ing-glafs, or Speftacle-glafs, or an Objedt-glafs of 
a Telefcope) and it be required to know how 
Light faUing upon it from any lucid point Q^ 
fhall be refra(5led, let Q^JVI reprefent a Ray 
falling upon any point M of its firfl fpherical 
Surface A C B, and by ered;ing a Perpendicular 
to the Glafs at the point M, find the firll re- 
fracted Ray M N by the Proportion of the 
Sines 17 to 11. Let that Ray in going out of 
the Glafs be incident upon N, and then find 
the fecond refraded Ray N q by the Propor- 
tion of the Sines 1 1 to 17. And after the fame 
manner may the Refradion be found when the 
Lens is convex on one fide and plane or con- 
cave on the other, or concave on both fides. 

A X. VI. 

Homogeneal Rays which foiD from feveral Points 
cf any Objecl^ and fall perpendicularly or almoji 
perpendicularly on any refieSiing or refraBing Flane 
or fpherical Surface^ Jhall afterwards diverge 
from fo many other Points^ or be parallel to Jo 
tnany other Lines, or converge to fo many other 
Points^ either accurately or without any fetifble 
'E,rror. And the fame thing will happen, if the 
Rays be refcBed or refracted fucceffively by two 
or three or more Plane or Spherical Surfaces. 

The Point from which Rays diverge or to 
which they converge may be called their Focus, 
And the Focus of the incident Rays being gi- 
I'cn, that of the refleded or refraded ones may 

be 



B O O K I. 9 

be found by finding the Refradtion of any two 
Rays, as above j or niore readily thus. 

Caf. I. Let ACB [in Fig. 4.] be a refleding or 
refradling Plane, and Q^he Focus of the incident 
Rays, and Q ^ C a Perpendicular to that Plane. 
And if this Perpendicular be produced to q^ 
fo that ^ C be equal to Q^, the Point q fhall 
be the Focus of the refledted Rays : Or if ^ C 
be taken on the fame fide of the Plane with 
Q^, and in proportion to Q^ as the Sine of 
Incidence to the Sine of Refra6tion, the Point q 
fliall be the Focus of the refracted Rays. 

Caf 2. Let ACB [in Fig. 5.] be the refleding 
Surface of any Sphere whofe Centre is E. Bi- 
fed: any Radius thereof, ( fuppofe EC) in T, 
and if in that Radius on the fame fide the Point 
T you take the Points Q^nd ^, fo that T Q^ 
T E, and T q^ be continual Proportionals, and 
the Point QJ)e the Focus of the incident Rays, 
the Point q fliall be the Focus of the refiedted 
ones. 

Caf. 3. Let ACB [in Fig. 6.] be the refnidting 
Surface of any Sphere whofe Centre is E. In 
any Radius thereof E C produced both ways 
take E T and C t equal to one another and fe- 
verally in fuch Proportion to that Radius as 
the lefi^er of the Sines of Incidence and P^e- 
fradion hath to the difference of thofe Sines. 
And then if in the fame Line you find any two 
Points Q^nd ^, fo that T QJ^e to E T as E /^ 
to / q^ taking t q the contrary way from / which 
T QJAeth from T, and if the Point QJ)e the 
Focus of any incident Rays, the Point q fliall be 
the Focus of the refracted ones> 

2 And 



lo O P T I C K S. 

And by the fame means the Focus of the Rays 
after two or more Reflexions or Refradions may 
be found. 

Caf.^. Let ACBD [in Fig. 7.] be any refrad- 
ing Lens , fpherically Convex or Concave or 
Plane on either fide, and let C D be its Axis 
( that is, the Line which cuts both its Surfaces 
perpendicularly, and paiTes through the Centres 
of the Spheres,) and in this Axis produced let 
F andybe the Foci of the refradled Rays found as 
above, w^hen the incident Rays on both iides the 
Lens are parallel to the fame Axis j and upon the 
Diameter F f bifecCled in E, defcribe a Circle. 
Suppofe now that any Point QJ>e the Focus of 
any incident Rsys. Draw QJ^ cutting the faid 
Circle in T and t^ and therein take t q m fuch 
proportion to / E as /^ E or T E hath to T Q^ 
Let / ^ lie the contrary way from t which T Q 
doth from T, and q fhall be the Focus of the, 
rcfrafted Rays without any 'fenfible Error, pro- 
vided the Point QJ)e not fo remote from the 
Axis, nor the Lens fo broad as to make any of 
the Rays fall too obliquely on the refracting 
Surfaces. * 

And by the like Operations may the reflecting 
or refracHiing Surfaces be found when the two 
Foci are given, and thereby a Lens be formed, 
which Ihall make the Rays flow towards or 
from what Place you pleafe. -f- 

* In our Author's LeEliones Optica:, Part I. Seft. IV. Prop. 29, 
30, there is an elegant Method of determining thefe Foci ; not only 
in fpherical Surfaces, but likewife in any other curved Figure what- 
ev«r : And in Prop. 32, 33, the fame thing is done tor any Ray ly- 
ing out of the Axis. 

f Ibid. Prop. ^4. 

. Sq 



B O O K I. It 

So then the Meaning of this Axiom is, that 
if Rays fall upon any Plane or Spherical Surface 
or Lens, and before their Incidence flow from 
or towards any Point Q^ they fhall after Re- 
flexion or Refra6lion flow from or towards the 
Point q found by the foregoing Rules. And if 
the incident Rays flow from or towards feveral 
points Q^ the refleded or refradled Rays fliall 
flow from or towards fo many other Points q 
found by the fame Rules. Whether the refle<5t- 
ed and refracted Rays flow from or towards the 
Point q is eafily known by the fltuation of that 
Point. For if that Point be on the fame flde 
of the refleding or refracting Surface or Lens 
with the Point Q^ and the incident Rays flow 
from the Point Q^ the reflected flow towards 
the Point q and the refradled from it ; and if the 
incident Rays flow towards Q, the refleded 
flow from q, and the refraded towards it. And 
the contrary happens when q is on the other 
fide of the Surface. 

A X. VIL 

Wherever the Rays which come from all the 
Points of any Object meet again in Jo many 
Poi?its after they have been made to converge by 
RefeBion or RefraBion^ there they will make a Pi' 
Bure of the ObjeB upon any white Body on which 
they fall. 

So if PR [in Fig. 3.] reprefent any Objed with- 
out Doors, and A B be a Lens placed at a hole 
in the Window-ihut of a dark Chamber, where- 
by the Rays that come from any Point Q^of 
I that 



12 O P T I C K S. 

that Qbje6t are made to converge and meet a- 
gain in the Point q j and if a Sheet of white Pa- 
per be held at q for the Light there to fall up- 
on it, the Pidlure of that Objed; P R will ap- 
pear upon the Paper in its proper jQiape and Co- 
lours. For as the Light which comes from the 
Point Q^goes to the Point q, fo the Light which 
comes from other Points P and R of the Objed:, 
will go to fo many other correfpondent Points 
p and r ( as is manifell by the fixth Axiom j ) fo 
that every Point of the Objed: fhall illuminate a 
correfpondent Point of the Pidure, and there- 
by make a Pidture like the Objed in Shape and 
Colour, this only excepted, that the Pidture fhall 
be inverted. And this is the Reafon of that vul- 
gar Experiment of cafting the Species of Objeds 
from abroad upon a Wall or Sheet of white Pa- 
per in a dark Room. 

In like manner, when a Man views any Objed: 
P QR, [in Fig. 8.] the Light which comes from 
the feveral Points of the Objed is fo refraded 
by the tranfparent fkins and humours of the 
Eye, (that is, by the outward coat E F G, called 
the "Tunica Corfiea, and by the cryftalline hu- 
mour A B which is beyond the Pupil ;;z ^ ) as to 
converge and meet again in fo many Points in 
the bottom of the Eye, and there to paint the 
Pidure of the Objed upon that fkin (called the 
Tunica Retina ) with which the bottom of the 
Eye is covered. For Anatomifts, when they have 
taken off from the bottom of the Eye that out- 
ward and moft thick Coat called the Dura Ma- 
ter^ can then fee through the thinner Coats, 
the Pidures of Objeds , lively paint^ there- 
on^ 



B O O K I. 13 

on. And thefe Pidlures, propagated by Mo- 
tion along the Fibres of the Optick Nerves in- 
to the Brain, are the caufe of Vilion. For ac- 
cordingly as thefe Pidtures are perfed: or im- 
perfedl, the Objed: is feen perfectly or imperfed:- 
ly. If the Eye be tinged with any colour (as in 
the Difeafe of the yawidice) fo as to tinge the 
Pidures in the bottom of the Eye with that 
Colour, then all Objeds appear tinged with the 
fame Colour. If the Humours of the Eye by 
old Age decay, fo as by (hrinking to make the 
Cornea and Coat of the Ci'yiialline Humour grow 
flatter than before, the Light will not be re- 
frad:ed enough, and for want of a fufficient Re- 
fraction will not converge to the bottom of the 
Eye but to fome place beyond it, and by con- 
fequence paint in the bottom of the Eye a con- 
fufed Pidlure, and according to the Indifl:in(ft- 
nefs of this Pidture the Objed: will appear con- 
fufed. This is the reafon of the decay of fight 
in old Men, and fhews why their Sight is mend- 
ed by Spedacles. For thofe Convex glalTes fup- 
ply the defed of plumpnefs in the Eye, and by 
increafing the Refradion make the Rays con- 
verge fooner, fo as to convene diftindly at the 
bottom of the Eye if the Glafs have a due de- 
gree of convexity. And the contrary happens 
in fhort-fighted Men whofe Eyes are too plump. 
For the Refradion being now too great, the 
Rays converge and convene in the Eyes before 
they come at the bottom > and therefore the 
Pidure made in the bottom and the Vifion 
caufed thereby will not be diftind, unlefs the 
Object be brought fo near the Eye as that the , 

place 



14 o p T I c k: s. 

place where the converging Rays convene may 
be removed to the bottom, or that the plump- 
nefs of the Eye be taken off and the Refrad:i- 
ons diminifhed by a Concave-glafs of a due de- 
gree of Concavity, or laflly that by Age the 
Eye grow flatter till it come to a due Figure: 
For fhort-fighted Men fee remote Objeds beft 
in Old Age, and therefore they are accounted to 
have the moft lafling Eyes. 

A X. VIII. 

An ObjeB fcen by Reflexion or "RefraSiion, ap' 
pears in that place from whence the Rays after their 
laji Reflexion or RefraBion diverge in falling on the 
SpeBators Eye, 

If the Object A [in Fig.^!\ be feen by Reflexion 
of a Looking-glafs m n^ it fliall appear, not in its 
proper place A, but behind the Glafs at a, from 
whence any Rays AB, AC, AD, which flow from 
one and the fame Point of the Objed, do after 
their Reflexion made in the Points B, C, D, di- 
verge in going from the Glafs to E, F, G, 
where they are incident on the Spectator's Eyes. 
For theJf^ Rays do make the fame Picture in the 
bottom of the Eyes as if they had come from 
the Objed: really placed at a without the Inter- 
pofition of the Looking-glafs; and all Vifion is 
made according to the place and fliape of that 
Pidure. 

In like manner the Obje6t D [in Fig. 2.] feen 
through a Prifm, appears not in its proper place 
D, but is thence tranflated to fome other place 
d fituated in the laft refraded Ray F G drawn 
backward from F to d. And 



B O O K I. 15 

And fo the'Objed: Q^[ in Fig. 10.] feentlirough 
tlie Lens A B, appears at the place q from whence 
the Rays diverge in paffing from the Lens to the 
Eye. Now it is to be noted, that the Image of 
the Objed; at q is fo much bigger or lelTer than 
the Objed: it felf at Q^, as the diftance of the 
Image at q from the Lens A B is bigger or lefs 
than the diftance of the Objed: at C^rom the 
fame Lens. And if the Objedl be feen through 
two or more fuch Convex or Concave-glafl'es, 
every Glafs fhall make a new Image, and the 
Object fhall appear in the pkce of the big- 
nefs of the laft Image. Which confideration un- 
folds the Theory of Microfcopes and Telefcopcs. 
For that Theory coniifts in almoll nothing elfe 
than the defcribing fuch Glafles as fliall make the 
laft Image of any Objedl as diHind and large and 
luminous as it can conveniently be made. 

I have now given in Axioms and their Ex- 
plications the fum of what hath hitherto been 
treated of in Opticks. For what hath been ge- 
nerally agreed on I content my felf to allume 
under the notion of Principles, in order to what 
I have farther to write. And this may fuffice 
for an Introdu6tion to Readers of quick Wit 
and good Underftanding not yet verfed in Op- 
ticks : Although thofe who are already acquaint- 
ed with this Science, and have handled GlalTes, 
will more readily apprehend what followeth. 



PROPO" 



O P T I C K S. 



PROPOSITIONS. 

P ROP.l T H E O R. I. 

T IG HTS which differ in Colour, differ alfo in 
Degrees of Refrangibility, 

The Proof by Experiments. 

Exper. I. I took a black oblong ftifF Paper 
terminated by Parallel Sides, and with a Per- 
pendicular right Line drawn crofs from one 
Side to the other, diftinguifhed it into two e- 
qual Parts. One of thefe parts I painted with 
a red colour and the other with a blue. The 
Paper was very black, and the Colours intenfe 
and thickJy laid on, that the Phaenomenon 
might be more confpicuous. This Paper I 
view'd through a Prifm of folid Glafs, wllofe 
two Sides through which the Light pafled to the 
Eye were plane and well polifhed, and contained 
an Angle of about fixty degrees ; which Angle 
I call the refracting; Angle of the Prifm. And 
whilft I view'd it, I held it and the Prifm before 
a Window in fuch manner that the Sides of the 
Paper were parallel to the Prifm, and both thofe 
Sides and the Prifm were parallel to the Horizon, 
and the crofs Line was*alfo parallel to it: and 
that the Light which fell from the Window upon 
the Paper made an Angle with the Paper, equal 
to that Angle which was made with the fame 

Paper 



B O O K I. J7 

Paper by the Light refle6led from It to the Eye. 
Beyond the Prifm was the Wall of the Chamber 
under the Window covered over with black 
Cloth, and the Cloth was involved in Darknefs 
that no Light might be reflected from thence, 
which in palTing by the Edges of the Paper to 
the Eye, might mingle itfelf with the Light of 
the Paper, and obfcure the Phaenomenon there- 
of. Thefe things being thus ordered, I found 
that if the refracting Angle of the Prifm be 
turned upwards, fo that the Paper may feem to 
be lifted upwards by the Refraction, its blue 
half will be lifted higher by the Refradlon ; ban 
its red half. But if the refrad:ing Angle of the 
Prifm be turned downward, fo that the Paper 
may feem to be carried lower by the Refra- 
d:ion, its blue half will be carried fomethin^ 
lower thereby than its red half Wherefore in 
both Cafes the Light which comes from the 
blue half of the Paper tlirough the Prifm to 
the Eye, does in like Circumitances fuffer a 
greater Refradion than the Light which comes 
from the red half, and by confequence is m.ore 
refrangible. 

Ilhijlration. In the eleventh Figure, M N 
reprefents the Window, and D E the Paper 
terminated with parallel Sides D J and H E, 
and by the tranfverfe Line F G diftinguiilied 
into two halfs, the one D G of an intenfely 
blue Colour, the other F E of an intenfely 
red. And ^ hC c a b reprefents the Prifm 
whofe refrading Planes KB b a and KC c a 
meet in the Edge of the refracting Angle *% a. 
This Edge A a being upward, is paralldftoth to 

C the 



i8 O P T I C K S. 

the Horizon, and to the Parallel-Edges of the 
Paper D J and HE, and the tranfverfe Line FG 
is perpendicular to the Plane of the Window. 
And de reprefents the Image of the Paper {0,^x1 
by Refraction upwards in fuch manner, that the 
blue half DG is carried higher to dg than the 
red half F E is to fe^ and therefore fuffers a 
greater Refrad:ion. If the Edge of the refracting 
Angle be turned downward, the Image of the 
Paper vv^ill be refraded downward j fuppofe to 
^ e, and the blue half will be refracted lower to 
^ y, than the red half is to 9 g. 

Exper, 2. About the aforeiaid Paper, whofe 
two halfs were painted over with red and blue, 
and which was ftifflike thin Pafteboard, I lapped 
feveral times a llender Thred of very black Silk, 
in fuch manner that the feveral parts of the 
Thred might appear upon the Colours like fo 
many black Lines drawn over them, or like 
long and {lender dark Shadows caft upon them. 
I might have drawn black Lines with a Pen, 
but the Threds were fmaller and better defined. 
This Paper thus coloured and lined I fet againft 
a Wall perpendicularly to the Horizon, fo that 
one of the Colours might ftand to the Right 
Hand, and the other to the Left. Clofe before 
the Paper, at the Confine of the Colours below, 
I placed a Candle to illuminate the Paper ftrong- 
ly : For the Experiment was tried in the Night. 
The Flame of the Candle reached up to the 
lower edge of the Paper, or a very little higher. 
Then at the diftance of fix Feet, and one or two 
Inches from the Paper upon the Floor I ereCted 
a Giafs Lens four Inches ajid a quarter broad, 

which 



B O O K I. x^ 

which might colled: the Rays coming from the 
feveral Points of the Paper, and make them con- 
verge towards fo many other Points at the fame 
diftance of fix Feet, and one or two Inches on 
the other fide of the Lens, and fo form the Image 
of the coloured Paper upon a white Paper placed 
there, after the fame manner that a Lens at a 
Hole in a Window cafts the Images of Objedts 
abroad upon a Sheet of white Paper in a dark 
Room. The aforefiid white Paper, ere<5i:ed per- 
pendicular to the Horizon, and to the Rays 
which fell upon it from the Lens, I moved 
fometimes towards the Lens, fometimes from 
it, to find the Places where the Images of the 
blue and red Parts of the coloured Paper appear- 
ed mojft diftindt. Thofe Places I eafily knew by 
the Images of the black Lines which I had made 
by winding the Silk about the Paper. For the 
Images of thofe fine and flender Lines (which 
by reafon of their Blacknefs were like Shadows 
on the Colours) were confufed and fcarce vifi- 
ble, unlefs when the Colours on either fide of 
each Line were terminated moft diftindlly. No- 
ting therefore, as diligently as I could, the 
Places where the Images of the red and blue 
halfs of the coloured Paper appeared mofl di- 
flindt, I found that where the red half of the 
Paper appeared diftindt, the blue half appeared 
confufed, fo that the black Lines drawn upon 
it could fcarce be feen ; and on the contrary, 
where the blue half appeared mofl diftindt, the 
red half appeared confufed, fo that the black 
Lines upon it were fcarce vifible. And between 
the two Places where thefe Images appeared 

C 3 diflindt 



2® O P T I C K S. 

diftind there was the diftance of an Inch atid a 
half; the diftance of the white Paper from the 
Lens, when the Image of the red. half of the co- 
loured Paper appeared moft diftind, being greater 
by an Inch and an half than the diftance of the 
fame white Paper from the Lens, when the Image 
of the blue half appeared moft diftind:. Irv 
like Incidences therefore of the blue and red 
upon the Lens, the blue was refradted more by 
the Lens than the red, fo as to converge fooner by 
an Inch and a half, and therefore is more refran- 
gible. 

Illiijlration. In the twelfth Figure, D E iig- 
nifies the coloured Paper, D G the blue half, 
FE the red half, MN the Lens, HJ the white 
Paper in that Place where the red half with its 
black Lines appeared diftind, and h i the fame 
Paper in that Place where the blue half appeared 
diftind:. The Place h i was nearer to the Lens 
M N than the Place H J by an Inch and an 
half 

^ Scholium. The fame Things fucceed, notwith- 
ftanding that fome of the Circumftances be va- 
ried y as in the firft Experiment when the Prifm 
and Paper are any ways inclined to the Hori- 
zon, and in both when coloured Lines are 
drawn upon very black Paper. But in the De- 
fcription of thefe Experiments, I have fet down 
fuch Circumftances, by which either the Phae- 
nomenon might be render'd more confpicuous, 
or a Novice might more eafily try them, or by 
which I did try them only. The fame Thing, I 
have often done in the following Experiments : 
Concerning all which, this one Admonition may 

fuffice. 



B O O K I. 2£ 

fuffice. Now from thefe Experiments It follows 
nor, that all the Light of the blue is more refran- 
gible than all the Light of the red : For both 
Lights are mixed of Rays differently refrangible, 
fo that in the red there are fome Rays not lefs re- 
frangible than thofe of the blue, and in the blue 
there are fome Rays not more refrangible than 
thofe of the red : But thefe Rays, in proportion to 
the whole Light, are but few, and ferve to dimi- 
nifh the Event of the Experiment, but are not 
able to deftroy it. For, if the red and blue Co- 
lours were more dilute and weak, the diflance of 
the Images would be lefs than an Inch and a half; 
and if they were more intenfe and full, that di- 
ftance would be greater, as will appear hereafter. 
Thefe Experiments may fuffice for the Colours of 
Natural Bodies. For in the Colours made by the 
Refradtion of Prifms, this Propof tion will ap- 
pear by the Experiments which are now to fol- 
low in the next Fropolition. 



PROP. 11. The OR. II. 

lie Light of the Sim confifls of Rajs 
differently Refrangible, 

The Proof by Experiments. 

Exper. 3. TN a very dark Chamber, at a round 
jj Hole, about one third Part of an 
Inch broaa, made in the Shut of a Window, I 
placed a Glafs Prifm, whereby the Beam of tlie 
Sun's Light, which came in at that Hole, might 
be refraj^ed upwards toward the oppofite \Vail 

C 3 of 



22 O P T I C K S. 

of the Chamber, and there form a colour'd I- 
mage of the Sun. The Axis of the Prifm ( that 
is, the Line paffing through the middle of the 
Prifm. from one end of it to the other end pa- 
rallel to the edge of the Refracting Angle ) was 
in this and the following Experiments perpen- 
dicular to the incident Rays. About this Axis 
I turned the Prifm flowly, and faw the refradt- 
ed Light on the Wall, or coloured Image of 
the Sun, firfl to defcend, and then to afcend. 
Between the Defcent and Afcent, when the I- 
mage feemed Stationary, I ftopp'd the Prifm, 
and fix'd it in that Pofture, that it fhould be 
moved no more. For in that Pofture the Re- 
fractions of the Light at the two Sides of the 
refracting Angle, that is, at the Entrance of the 
Rays into the Prifm, and at their going out of 
it, were equal to one another*. So alfo in other 
Experiments, as often as I would have the Re-' 
fractions on both fides the Prifm to be equal to 
one another, I noted the Place where the Image 
of the Sun formed by the refraCted Light ftood 
ftill between its two contrary Motions, in the 
common Period of its Progrefs and Regrefs ; and 
when the Image fell upon that Place, I made 
faft the Prifm. And in this Pofture, as the moft 
convenient, it is to be underftood that all the 
Prifms are placed in the following Experiments, 
unlefs where fome other Pofture is defcribed. 
The Prifm therefore being placed in this Po- 
fture, I let the refracted Light fall perpendicu- 
larly upon a Sheet of white Paper at the oppo- 
fite Wall of the Chamber, and obferved the Fi- 

* See eur AuthorV Leftiones Optica, Parti. Se£i. i. § !©• 
StU, II. § 29. and SeSl. III. frop. 25. gurc 



B O O K I. Q3 

gure and Dimenrions of the Solar Image form- 
ed on the Paper by that Light. This Image 
was Oblong and not Oval, but terminated with 
two Rectilinear and Parallel Sides, and tv/o Se- 
micircular Ends. On its Sides it was bounded 
pretty diftindtly, but on its Ends very confuled- 
ly and indiftindly, the Light there decaying 
and vanifl:iing by degrees. The Breadch of this 
Image anfwered to the Sun's Diam.eter, and was 
about two Inches and the eighth Part of an 
Inch, including the Penumbra. For the Image 
was eighteen Feet and an half dlftant from the 
Prifm, and at this diftance that Breadth, if di- 
minifhed by the Diameter of the Hole in the 
Window-fhut, that is by a quarter of an Inch, 
fubtended an Angle at the Prifm of about half 
a Degree, which is the Sun's apparent Diame- 
ter. But the Length of rhe Image was about ten 
Inches and a quarter, and the Length oi the Re- 
d-ilinear Sides about eight Inches ; and the re- 
fracting Angle of the Prifm, whereby fo great a 
Length was made, was 64 degrees. With a lefs 
Angle the Length of the Image was lefs, the 
Breadth remaining the fame. If the Prifm was 
turned about its Axis that way which made the 
Rays emerge more obliquely out of the fecond 
refracting Surface of the Prifm, the Image foon 
became an Inch or two longer, or morej and 
if the Prifm was turned about the contrary 
way, fo as to make the Rays fall more obliquely 
on the firft refraCting Surface, the Image fooa 
became an Inch or two fhorter. And there- 
fore in trying this Experiment, I was as curi- 
Qus as I could be in placing the Prifm by xhe 

C 4 abo\^* 



24 O P T I C K S. 

above-mention'd Rule exadtly in fuch a Poflure, 
that the Refradions of the Rays at their Emer- 
gence out of the Prifm might be equal to that 
at their Incidence on it. This Prifm had fome 
Veins running along within the Glafs from one 
end to the other, which fcattered fome of the 
Sun's Light irregularly, but had no fenfible Ef- 
fect in increafing the Length of the coloured 
Spedirum. For I tried the fame Experiment 
with other Prifms with the fame Succefs. And 
particularly with a Prifm which feemed free 
from fuch Veins, and whofe refracting Angle 
was 625 Degrees, I found the Length of the 
Image 95 or 10 Inches at the diflance of i8| 
Feet from the Prifm, the Breadth of the Hole 
in the Window-fhut being J of an Inch, as be- 
fore. And becaufe it is eaiy to commit aMi- 
llake in placing the Prifm in its due Pofture, I 
repeated the Experiment four or five Times, 
and always found the Length of the Image that 
which is fet down above. With another Prifm 
of clearer Glafs and better Polifh, which feem- 
ed free from Veins, and whofe refracting Angle 
was 631 Degrees, the Length of this Image at 
the fam^e diftance of i8i Feet was alfo about 10 
Inches, or loi Beyond thefe Meafures for a- 
bout a : or i of an Inch at either end of the 
SpeCtrum the Light of the Clouds feemed to be a 
little tinged with red and violet, but fo very 
faintly, that I fufpeded that TinCture might ei- 
ther v/holly, or in great Meafure arife from fome 
Rays of the Spedtrum fcattered irregularly by 
fome Inequalities in the Subftance and Polilli of 
the Glafs, and therefore I did not include it in 
I tliefe 



B O O K I. 25 

thefe Meafures. Now the different Magnitude 
of the hole in the Window-fhut, and different 
thicknefs of the Prifm where the Rays palled 
through it, and different inclinations of the 
Prifm to the Horizon, made no fenfible chan- 
ges in the length of the Image. Neither did 
the different matter of the Prifms make any: 
for in a Veffel made of polifhed Plates of Glafs 
cemented together in the fhape of a Prifm and 
filled with Water, there is the like Succefs of 
the Experiment according to the quantity of 
the Refradlion. It is farther to be obferved, 
that the Rays went on in right Lines from the 
Prifm to the Image, and therefore at their very 
going out of the Prifm had all that Inclina- 
tion to one another from which the length of 
the Image proceeded, that is, the Inclination of 
more than two degrees and an half. And yet 
according to the Laws of Opticks vulgarly re- 
ceived, they could not poffibly be fo much incli- 
ned to one another *. For let E G [ mFig. 1 3.] re- 
prefent the Window-fhut, F the hole made there- 
in through which a beam of the Sun's Light 
was tranfmitted into the darkned Chamber, and 
ABC a Triangular Imaginary Plane whereby the 
Prifm is feigned to be cut tranfverfly through 
the middle of the Light. Or if you pleafe, let 
ABC reprefent the Prifm it felf, looking di- 
redtly towards the Speftator's Eye with its nearer 
end; And let X Y be the Sun, MN the Pa- 
per upon which the Solar Image or Spectrum is 
caff, and P T the Image it felf whofe fides to- 
wards 1; and w are Redlilinear and Parallel, and 
ends towards P and T Semicircular. YKHP 

and 

* See OMx Author's Lenionei Opticcy Part. I. Sect. i. §.5. 



^6 d p T I c K a 

and X L J T are two Rays, the firft of. which 
comes from the lower part of the Sun to the 
higher part of the Image, and is refraded in the 
Prifm at K and H, and the latter comes from 
the higher part of the Sun to the lower part of 
the Image, and is refradted at L and J. Since 
the Refradions on both fides the Prifm are e- 
qual to one another, that is, the Refraction at 
K equal to the Refradion at J, and the Refra- 
dion at L equal to the Refradion at H, fo that 
the Refradions of the incident Rays at K and L 
taken together, are equal to the Refradions of 
the emergent Rays at H and J taken together : 
it follows by adding equal things to equal things, 
that the Refradions at K and H taken together, 
are equal to the Refradions at J and L taken 
together, and therefore the two Rays being e- 
qually refraded, have the fame Inclination to 
one another after Refradion which they had 
before ; that is, the Inclination of half a Degree 
anfwering to the Sun's Diameter. For fo great 
was the Inclination of the Rays to one another 
before Refradion. So then, the length of the 
Image P T would by the Rules of Vulgar Op- 
ticks fubtend an Angle of half a Degree at the 
Prifm , and by Confequence be equal to the 
breadth 'y w -, and therefore the Image would 
be round. Thus it would be were the two 
Rays XL JT and YKHP, and all the reft which 
form the Image P w T 'u, alike refrangible. 
And therefore feeing by Experience it is found 
that the Image is not round, but about five times 
longer than broad, the Rays which going to the 
upper end P of the Image fuffer the greateft Re- 
fradion, 



BOOK I. a; 

fradion, mufl be more refrarxgible than thofe 
which go to the lower end T, unlefs the Inequa- 
lity of Refradtion be cafual. 

This Image or Spectrum P T was .coloured, 
being red at its leaft refradled end T, and vio- 
let at its moil refraded end P , and yellow 
green and blue in the intermediate Spaces. 
Which agrees with the firft Proportion, that 
Lights which differ in Colour, do alio differ in 
Refrangibility. The length of the Image in the 
foregoing Experiments, I meafured from the 
fainteft and outmoft red at one end, to the 
fainteft and outmoft blue at the other end, ex- 
cepting only a little Penumbra, whofe breadth 
fcarce exceeded a (quarter of an Inch, as was 
faid above. 

Exper. 4. In the Sun's Beam which was pro- 
pagated into the Room through the hole in the 
Window-fhut , at the diffance of fome Feet 
from the hole, I held the Prifm in fuch a Po- 
llure, that its Axis might be perpendicular to 
that Beam. Then I looked through the Prifm 
upon the hole, and turning the Prifm to and 
fro about its Axis, to rhake the Image of the 
Hole afcend and defcend-, when between its 
two contrary Motions it feemed Stationary, I 
ftopp'd the Prifm, that the Refradions of both 
fides of the refrading Angle might be equal to 
each other, as in the former Experiment. In 
this Situation of the Priim viewing through it 
the faid Hole, I obferved the length of its re- 
fraded Image to be many times greater than 
its breadth, and that the moH: refraded part 
■ thereof appeared violet, the lead refraded red, 
2 the 



28 O P T I C K S. 

the middle parts blue, green and yellow in or- 
der. The fame thing happen'd when I remo- 
ved the Prifm out of the Sun's Light, and look- 
ed through it upon the hole fliining by the 
Light of the Clouds beyond it. And yet if the 
Refradtion were done regularly according to 
one certain Proportion of the Sines of Inci- 
dence and Refradion as is vulgarly fuppofed, 
the refraded Image ought to have appeared 
round. 

So then, by thefe two Experiments it appears, 
that in equafi Incidences there is a confiderable 
inequality of Refractions. But whence this in- 
equality arifes, whether it be that fome of the 
incident Rays are refradled more, and others lefs, 
conftantly, or by chance, or that one and the 
fame Ray is by Refrad;ion difturbed, fliatter'd, 
dilated , and as it were fplit and fpread into ma- 
ny diverging Rays, as Grimaldo fuppofes, does 
not yet appear by thefe Experiments, but will 
appear by thofe that follow. 

Exper. 5. Confidering therefore, that if in 
the third Experiment the Image of the Sun 
jfhould be drawn out into an oblong Form, ei- 
ther by a Dilatation of every Ray, or by any o- 
ther cafual inequality of the Refradions, the 
fame oblong Image would by a fecond Refra- 
dion made fideways be drawn out as much in 
breadth by the like Dilatation of the Rays, or o- 
ther cafual inequality of the Refradions fide- 
ways, I tried what would be the Effeds of fuch 
a fecond Refradion. For this end I ordered 
all things as in the third Experiment, and then 
placed a fecond Prifm immediately after the 

firfl 



B O O K L 2p 

I firfl: in a crofs Pofition to it, that it might again 
refrad; the beam of the Sun*s Light which came 
to it through the firfl: Prifm. In the firfl Prifm 
this beam was refracted upwards, and in the 
fecond fideways. And I found that by the Re- 
fraction of the fecond Prifm, the breadth of the 
Image was not increafed, but its fuperior part, 
which in the firfl Prifm fuffered the greater Re- 
fradlion, and appeared violet and blue, did again 
in the fecond Prifm fuffer a greater Refradlion 
than its inferior part, which appeared red and 
yellow, and this without any Dilatation of the 
Image in breadth. 

Illiijiration. Let S [in Fig. 14. ] reprefent 
the Sun, F the hole in the Window, ABC tlie 
iirfl Prifm, D H the fecond Prifm, Y the round 
Image of the Sun made by a diredl beam of 
Light when the Prifms are taken away, P T 
the oblong Image of the Sun made by that beam 
pafling through the firfl Prifm alone, when the 
fecond Prifm is taken away, and p t the Image 
made by the crofs Refradions of both Prifms 
together. Now if the Rays which tend to- 
wards the feveral Points of the round Image Y 
were dilated and fpread by the Refraction of 
the firfl Prifm, fg that they fhould not any lon- 
ger go in fmgle Lines to fingle Points, but that 
every Ray being fplit, fliattered, and changed 
from a Linear Ray to a Superficies of Rays di- 
verging from the Point of Refraction, and ly- 
ing in the Plane of the Angles of Incidence and 
Refraction, they fhould go in thofe Planes to 
fo many Lines reaching almofl from one end of 
the Image P T to the other, and if that Image 

fhould 



50 ' OP T I C K S. 

fhould thence become oblong: thofe Rays and 
their feveral parts tending towards the feveral 
Points of the Image P T ought to be again di- 
lated and fpread fide ways by the tranfverfe 
Refraftion of the fecond Prifm, fo as to com- 
pofe a four fquare Image, fuch as is reprefented 
at iH. For the better underftanding of which, 
let the Image P T be diftinguiflied into five e- 
qual parts P QK, KQRL, LRSM, MSVN, 
N VT. And by the fame irregularity that the 
orbicular Light Y is by the Refraction of the 
firft Prifm dilated and drawn out into a long 
Image P T, the Light P QK which takes up a 
fpace of the fame length and breadth with the 
Light Y ought to be by the Refraftion of the 
fecond Prifm dilated and drawn out into the 
long Image tt q k p, and the Light K QjR. L into 
the long Image kqrl, and the Lights LRSM, 
MSVN, N V T, into fo many other long I- 
mages /r ^?;7, ?nsvny nvtl, and all thefe long 
Images would compofe the four fquare Image 
•TT?. Thus it ought to be were every Ray dila- 
ted by Refraction, and fpread into a triangular 
Superficies of Rays diverging from the Point 
of Refradlion. For the fecond Refradion 
would fpread the Rays one way as much as the 
firft doth another, and fo dilate the Image in 
breadth as much as the firft doth in length. 
And the fame thing ought to happen , were 
fome Rays cafually refradled more than others. 
But the Event is other wife. The Image P T 
was not made broader by the Refraction of the 
fecond Prifm., but only became oblique, as 'tis 
reprefented at / ^ , its upper end P being by 

the 



B O O K I. 31 

the Refradion tranflatedto a greater diftance than 
its lower end T. So then the Light which went 
towards the upper end P of the Image, was ( at 
equal Incidences ) more refraded in the fecond 
Prifm, than the Light which tended towards the 
lower end T, that is the blue and violet, than the 
red and yellow j and therefore was more refran- 
gible. The fame Light was by the Refradion of 
the iirft Prifm tranflated farther from the place. 
Y to which it tended before Refraction ; and 
therefore fuffered as well in the firft Prifm as in 
the fecond a greater Refradion than the reft of 
the Light, and by confequence was more refran- 
gible than the reft, even before its incidence on 
the firft Prifm. 

Sometimes I placed a third Prifm after the 
fecond, and fometimes alfo a fourth after the 
third, by all which the Image might be often 
refraded fideways: but the Rays which were 
more refradted than the reft in the firft Prifm 
were alfo more refraded in all the reft, and that 
without any Dilatation of the Image fideways : 
and therefore thofe Rays for their conftancy of a 
greater Refraction are defervedly reputed more 
refrangible. 

But that the meaning of this Experiment may 
more clearly appear, it is to be confidercd that 
the Rays which are equally refrangible do fall 
upon a Circle anfwering to the Sun's Difque. 
For this was proved in the third Experiment. 
By a Circle I underftand not here a perfect geo- 
metrical Circle, but any orbicular Figure whofe 
length is equal to its breadth,' and which, as 
to Senfe, may feem circular. Let therefore A G 

[in 



32 O P T I C K S. 

[in Fig. 15.] reprefent the Circle which all the 
niofl: refrangible Rays propagated from the 
whole Difque of the Sun, would illuminate and 
paint upon the oppofite Wall if they were a- 
lonej E L the Circle which all the leafl refran- 
gible Rays would in like manner illuminate and 
paint if they were alone; B H, C J, DK, the 
Circles which fo many intermediate forts of 
Rays would fucceffively paint upon the Wall, 
if they were fmgly propagated from the Sun 
in fucceflive order, the reft being always inter- 
cepted ; and conceive that there are other in* 
termediate Circles without Number , which 
innumerable other intermediate forts of Rays 
would fucceffively paint upon the Wall if the 
Sun fliould fucceffively emit every fort apart. 
And feeing the Sun emits all thefe forts at once, 
they muft all together illuminate and paint in- 
numerable equal Circles, of all which, being 
according to their degrees of Refrangibility 
placed in order in a continual Series, that ob- 
long Spedrum P T is compofed which I defcri- 
bed in the third Experiment. Now if the 
Sun's 'circular Image Y [in Fig. 14, 15.] which 
is made by an unrefradled beam of Light was 
by any Dilation of the fnigle Rays, or by any 
other irregularity in the Refra<5lion of the iirft 
Prifm, converted into the oblong Spedtrum, 
P T : then ought every Circle AG, B H, C J, 
^c. in that Spedtrum, by the crofs Refradion 
of the fecond Prifm again dilating or other wife 
fcattering the Rays as before, to be in like man- 
ner drawn out and transformed into an oblong 
Figure, and thereby the breadth of the Image 

" FT 



B O O K I. 3 3 

PT would be now as much augmented as tlie 
length of the Image Y was before by the Refra- 
dionof the firftPrifmj and thus by the Refra- 
ctions of both Prifms together would be formed 
a four fquare Figure p ir t% as I defcribed a- 
bove. Wherefore fmce the breadth of the Spe- 
drum PT is not increafed by the Refradion 
fideways, it is certain that the Rays are nqt fplit 
or dilated, or otherways irregularly fcatter'd 
by that Refradtion, but that every Circle is by 
a regular and uniform Refradion tranflated 
entire into another Place, as the Circle AG 
by the greateft Refradion into the place a gy 
the Circle B H by a lefs Refradioh into the 
place b h, the Circle C J by a Refradion ftill 
lefs into the place c i, and fo of the reft) by 
which means a new Spedrum p t inclined to 
the former P T is in like manner compofed of 
Circles lying in a right Line ; and thefe Circles 
muft be of the fame bignefs with the former, 
becaufe the breadths of all the Spedrums Y, 
P T and /> / at equal diftances from the Prifms 
are equal. 

I conlidered farther, tliat by the breadth of 
the hole F through which the Light enters in- 
to the dark Chamber , there is a Penumbra 
made in the Circuit of the Spedrum Y, and 
that Penumbra remains in the redilinear Sides 
of the Spedrums P T and pt. I 'placed there- 
fore at that hole a Lens or Objed-glafs of a Te- 
lefcope w^hich might caft the Image of the Sun 
diftindly on Y without any Penumbra at all, 
and found that the Penumbra of the redilinear 
Sides of the oblong Spedrums P T and / 1 was 

D alfo 



34 O P T I C K S. 

alfu thereby taken away, fo that thofe Sides ap- 
peared as diilindily defined as did the Circum- 
ference of the firft Image Y. Thus it happens 
if the Glafs of the Prifms be free from Veins, 
and their Sides be accurately plane and well 
polifhed without thofe numberlefs Waves or 
Curies which ufually arife from Sand-holes a 
little fmoothed in polilliing with Putty. If the 
Glafs be only well polifhed and free from Veins, 
and the Sides not accurately plane, but a little 
Convex or Concave, as it frequently happens; 
yet may the three Spedtrums Y, P T and p t 
want Penumbras , but not in equal diftances 
from the Prifms. Now from this want of Pe- 
numbras, I knew more certainly that every one 
of the Circles v/as refracted according to fome 
inoft regular, uniform and conftant Law. For 
if there were any irregularity in the Refra(5tion, 
rhe right Lines A E and G L, which all the Cir- 
cles in the Spe6lrum P T do touch, could not 
by that Refraction be tranflated into the Lines 
a e and ^ / as diflind: and fcraight as they were 
before, but there would arife in thofe tranflated 
Lines fome Penumbra or Crookednefs or Un- 
dulation, or other fenfible Perturbation contrary 
to what is found by Experience. Whatfoever 
Penumbra or Perturbation fhould be made in the 
Circles by the crofs Refraction of the fecond 
Prifm, all that Penumbra or Perturbation would 
be confpicuous in the right Lines ae and gl 
which touch thofe Circles. And therefore fince 
there is no fuch Penumbra or Perturbation in 
thofe right Lines, there muft be none in the Cir^ 
cles. Since the difbance between thofe Tangents 

■2 or 



B O O K r. 35 

or breadth of the Spedrum is not increafed 
by the Refra<5tions, the Diameters of the Circles 
are not increafed thereby. Since thofe Tangents 
continue to be right Lines, every Circle wiiich 
in the iirft Prifm is more or lefs refraded, is 
exactly in the fame proportion more or lefs re- 
fracted in the fecond. And feeing all thefe 
things continue to fucceed after the lame man- 
ner when the Rays are again in a third Prifm, 
and again in a fourth refra6led fideways, it is 
evident that the Rays of one and the fame Circle, 
as to their degree of Refrangibility, continue al- 
ways uniform and homogeneal to one another, 
and that thole of feveral Circles do differ in de- 
gree of Refrangibility, and that in fome certain 
and conflant Proportion. Which is the thing I 
was to prove. 

There is yet another Clrcumflance or two of 
this Experiment by which it becomes Hill more 
plain and convincing. Let the fecond Prifm 
DH [in Fig, i6.] be placed not immedi- 
ately after the firlt , but at fome diftance 
from it; fuppofe in the mid-way between it 
and the Wall on which the oblong Spe<5truni 
PT is caft, fo that the Light from the firft 
Prifm may fall upon it in the form of an ob- 
long Spedrum -r^ parallel to this fecond Prifm, 
and be refraded tideways to form the oblong 
Spedrum pt upon the Wall. And you- will 
find as before, that this Spedirum /> / is inclined 
to that Spedrum P T, which the firft Prifm 
forms alone without the fecond; the blue ends 
P and p being farther diftant from one another 
than the red ones T and /, and by confequence 

D 2 ' that 



3^ O P T I C K S. 

that the Rays which go to the blue end cr of 
the Image <t 7, and which therefore fuffer the 
greateft Refradion in the firft Prifm, are again 
in the fecond Prifm more refradied than the 
reft. 

The fame thing I try'd alfo by letting the 
Sun's Light into a dark Room through two lit- 
tle round holes F and (p [in Fig. 17.] made in 
the Window , and with two parallel Prifms 
ABC and a/Sy placed at thofe holes ( one at 
each ) refra6ting thofe two beams of Light to 
the oppofite Wall of the Chamber, in fuch man- 
ner that the tv/o colour'd Images P T and M N 
which they there painted were joined end to end 
and lay in one flraight Line, the red end T of 
the one touching the blue end M of the other. 
For if thefe two refracfted Beams were again. 
by a third Prifm DH placed crofs to the two 
firft , refraded fideways , and the Spedlrums 
thereby tranilated to fome other part of the 
Wall of the Chamber, fuppofe the Sped:rum 
P T to pt and the Spedrum M N to m ;/, thefe 
tranflated Spedrums p t and. m n would not lie 
in one ftraight Line with their ends contiguous 
as before, but be broken oif from one another 
and become parallel, the blue end m of the I- 
mage m n bein^ by a greater Refradion tran- 
flated farther from its former place M T, than 
the red end t of the other Image p t from the 
fam.e place M T ; which puts the Propofition 
pad Difpute. And this happens whether the 
third Prifm D H be placed immediately after 
the two firft, or at a great diftance from 
them, fo that the Light refraded in the two 

firfl 



B O O K I. ' 37 

iirft Prifms be either white and circular, or co- 
loured and oblong when it falls on the third. 

^xper. 6. In the middle of two. thin Boards 
I made round holes a third part of an Inch in 
diameter , and iri the Window-fliut a much 
broader hole being made to let into my dark- 
ned Chamber a large Beam of the Sun's Light; 
I placed a Prifm behind the Shut in that beam 
to refradl it towards the oppofite Wali, and 
clofe behind the Prifm I fixed one of the Boards, 
in fuch manner that the middle of the refradled 
Light might pafs through the hole made in it, 
and the reft be intercepted by the Board. Then 
at the diftance of about twelve Feet from the 
firft Board I fixed the other Board in fuch man- 
ner, that the middle of the refraded Light which 
canie through the hole in the firft Board, and 
fell upon the oppofite Wall, might pafs through 
the hole in this other Board , and the reft being 
intercepted by the Board might paint upon it 
the coloured Spectrum of the Sun. And clofe 
behind this Board I fixed another Prifm to rc- 
fra<ft the Light v/hich came through the hole. 
Then I returned fpeedily to the firft Prifm, and 
by turning it llowly to and fro about its Axis, 
I caufed the Image which fell upon the fecond 
Board to move up and down upon that Board, 
that all its parts might fucceflively pafs through 
the hole in that Board and fall upon the Prifm 
behind it. And in. the mean time, I noted the 
places on the oppofite Wall to which that Light 
after its Refraftion in the fecond Prifm did pafs ; 
and by the difference of the places I found that 
the Light which being ir.olt refraded in the 

JD 3 firft 



38 O P T I C K S. 

firfl Prifm did go to the blue end of the Image, 
was again more refraded in the fecond Prifm 
than the Light which went to the red end of 
that Image, which proves as well the firfl Pro- 
portion as the fecond. And this happened whe- 
ther the Axis of the two Prifms were parallel, or 
inclined to one another, and to the Horizon in 
any given Angles. 

TUnJlration. Let F \\xs.Fig. i8.] be the wide 
hole in the Window-ihut, through which the 
Sun fliines upon the firfl Prifrii ABC, and let 
the refracted Light fall upon the middle of the 
Board D E, and the middle part of that Light 
upon the hole G made in the middle part of that 
Board. Let this trajed:ed part of that Light 
fall again upon the middle of the fecond Board 
d e, and there paint fuch an oblong coloured I- 
mage of the Sun as was defcribed in the third 
Experiment. By turning the Prifm ABC flow- 
iy to and fro about its Axis, this Image will be 
made to move up and down the Board de, 
and by this means all its parts from one end to 
the other may be made to pafs fucceffively 
through the hole g which is made in the mid- 
dle of that Board. In the mean while another 
Prifm abcisto be fixed next after that hole gy 
to refrad: the trajed:ed Light a fecond time. 
And thefe things being thus orderea, I marked 
the places M and N of the oppofite Wall upon 
which the refracted Light fell, and found that 
whilft the two Boards and fecond Prifm re- 
mained unmoved, thofe places by turning the 
firfl: Prifm about its Axis were changed perpe- 
tually. For when the lower part of the Light 

which 



B O O K I. 3p 

which fell upon the fecond Board d e \vas call 
through the hole g, it went to a lower place M 
on the Wall, and when the higher part of that 
Light was caft through the fame hole o-, it went 
to a higher place N on the Wall, and wheii any 
intermediate part of the Light was caft through 
that hole, it went to fome place on the Wall be- 
tween M and N. The unchanged Pofition of 
the holes in the Boards, made the L^cidence 
of the Rays upon the fecond Prifm to be the 
fame in all cafes. And yet in that common In- 
cidence fome of the Rays were more refra(5tcd, 
and others lefs. , And thofe were more refraded 
in this Prifm, which by a greater Refradion in 
the firft Prifm were more turned out of the 
way, and therefore for their Conftancy of being 
more refradied are defervedly called more refran- 
gible. 

Exper. J. At two holes made near one ano- 
ther in my Window- fliut I placed two Prifms, 
one at each, which nii?;ht caft upon the oppo- 
fite Wall (after the manner of the third Expe- 
riment) two oblong coloured Luages of the 
Sun. And at a little diftance from the Wall I 
placed a long (lender Paper with ftraight and pa- 
rallel edges, and ordered the Prifms and Pa- 
per fo, that the red Colour of cneiCmage might 
fall diredly upon one half of the Paper, and 
the violet Colour of the other Image upon the 
other half of the fame Paper ; fo that the Pa- 
per appeared of two Colours, red and violet, 
much after the manner of the painted Paper 
in the firft and fecond Experiments. Then 
with a black Cloth I covered the Wall behind 

D 4 thQ 



40 O P T I C K S. 

the Paper, that no Light might be refledied from 
it to difliirb the Experiment, and viewing the 
Paper through a third Prifm held parallel to it, 
I faw that half of it which was illuminated by 
the violet Light to be divided from the other 
half by a greater Refra(5lion, efpecially when I 
went a good way off from the Paper. For 
when I viewed it too near at hand, the two halfs 
of the Paper did not appear fully divided from 
one another, but feemed contiguous at one of 
their Angles like the painted Paper in the firft 
Experiment. Which alfo happened when the 
Paper was too broad. 

Sometimes inftead of the Paper I ufed a white 
Thred, and this appeared through the Prifm 
divided into two parallel Threds as is repre- 
fented in the nineteenth Figure , where D G 
denotes the Thred illuminated with violet Light 
from D to E and with red Light from F to G, 
and d e fg are the parts of the Thred feen by 
Refradion. If one half of the Thred be con- 
ftanrly illuminated v/ith red, and the other half 
be ilkuninated with all the Colours fucceffively, 
( which may be done by caufing one of the 
Prifms to be turned about its Axis whilft the 
other remains unmoved) this other half in view- 
ing the Thred through the Prifm, will appear 
in a continual right Line with the firfl half when 
illuminated with red, and begin to be a little 
divided from it when illuminated with Orange, 
jind remove farther from it when illuminated 
yvith yellow, and ftill farther when with green, 
^nd farther when with blue, and go yet farther 
pff when illuriiinated with Iiidigo, and fartheft 

when 



B O O K L 41 

when with deep violet. Which plainly fhews, 
that the Lights of feveral Colours are more and 
more refrangible one than another, in this Order 
of their Colours, red, orange, yellow, green, 
blue, indigo, deep violet j and fo proves as well 
the firft Proportion as the fecond. 

I caufed alfo the coloured Spedrums P T 
[ in Fig. ij. ] and M N made in a dark Cham- 
ber by the Refradions of -two Prifms to lie in 
a Right Line end to end, as was defcribed above 
in the fifth Experiment, and viewing them 
through a third Prifm held parallel to their 
Length, they appeared no longer in a Right 
Line, but became broken from one another, as 
they are reprefented at ^ ^ and ;;/ ;/, the violet 
end m of the Specftrum m n being by a greater 
Refradion tranllated farther from its former 
Place M T than the red end t of the other 
Spedrum pt. 

I farther caufed thofe two Spedtrums P T 
[ in Fig. 20. ] and M N to become co-incident 
in an inverted Order of their Colours, the red 
end of each falling on the violet end of the o- 
ther, as they are reprefented in the oblong Fi- 
gure PTMN J and then viewing them through 
a Prifm D H held parallel to their Length, they 
appeared not co-incident, as when view'd with 
the naked Eye, but in the form of two diftindt 
Spedrums p t and m n croffing one another in 
the middle after the manner of the Letter X. 
"Which fliews that the red of the one Spedrum 
and violet of the other, which were co-incident 
at PN and MT, being parted from one another 
by a greater Refradipn of the violet to p and m 

thau 



42 O P T I C K S. 

than of the red to n and /, do differ in degrees of 
Refrangibility. 

I illuminated alfo a little Circular fiece of 
white Paper all over with the Lights of both 
Prifms intermixed, and when it was illumina- 
ted with the red of one Speftrum, and deep 
violet of the other, fo as by the Mixture of 
thofe Colours to appear all over purple, I view- 
ed the Paper, firft at a lefs diflance, and then 
at a greater, through a third Prifmj and as I 
went from the Paper, the refracted Image there- 
of became more and more divided by the une- 
qual Refraction of the two mixed Colours, and 
at length parted into two diftind: Images, a red 
one and a violet one, whereof the violet v/as 
fartheft from the Paper, and therefore fuffered 
the greateft Refraction. And when that Prifm 
at the Window, which caft the violet on the Pa- 
per was taken away, the violet Image difiip- 
peared ; but when the other Prifm was taken 
away the red vaniflied ; which fhews, that thefe 
two Images were nothing elfe than the Lights 
of the two Prifms, which had been intermixed 
on the purple Paper, but were parted again by 
their unequal Refradions made in the third 
Prifm, through which the Paper was view'd. 
This alfo was obfervable, that if one of the 
Prifms at the Window, fuppgfe that which caft 
the violet on the Paper, v/as turned about its 
Axis to make all the Colours in this order,- vio- 
let, indigo, blue, green, yellow, orange, red, 
fall fucceffively on the Paper from that Prifm, 
the violet Image changed Colour accordingly, 
turning fucceffively to indigo, blue, green, yel- 
low 



B O O K ^. 45 

low and red, and in changing Colbur came nearer 
and nearer to the red Image made by the other 
Prifm, until when it was alfo red both Images be- 
came fully co-incident. 

I placed alfo tv/o Paper Circles very near one 
another, the one in the red Light of one Prifm, 
and the other in the violet Light of the other. 
The Circles were each of tliem an Inch in diame- 
ter, and behind them the Wall was dark, that- the 
Experiment might not be diflurbed by any Light 
coming from thence. Thefe Circles thus illu* 
minated, I viewed through a Prifm fo held, that 
the Refradlion might be made towards the red 
Circle, and as 1 went from them they came nearer 
and nearer together, and at length became co- 
incident } and afterwards when I went flill far- 
ther off, they parted again in a contrary Order, 
the violet by a greater Refradtion being carried 
beyond the red. 

Exper. 8. In Summer, when the Sun's Light 
ufes to be ftrongefl, I placed a Prifm at the 
Hole of the Window-fliut, as in the third Expe- 
riment, yet fo that its Axis might be parallel to 
the Axis of the. World, and at the oppofite 
Wall in the Sun's refrad:ed Light, I placed an 
open Book. Then going fix Feet and two Inches 
from the Book, 1 placed there the above- 
mentioned Lens, by which the Light reflected 
from the Book might be made to converge and 
meet again at the diftance of fix Feet and two 
Inches behind the Lens, and there paint the 
Species of the Book upon a Sheet of white Pa- 
per much after the manner of the fecond Ex- 
periment. The Book and Lens being made fall, 

I no- 



44 O P T I C K S. 

I noted the Place where the Paper was, when 
the Letters of the Book, illuminated by the 
fuUeft red Light of the Solar Image falling upon 
it, did cafl their Species on that Paper moft 
diftinftly : And then I ftay'd till by the Motion 
of the Sun, and confequent Motion of his Image 
on the Book, all the Colours from that red to 
the middle of the blue pafs'd over thofe Let- 
ters J and when thofe Letters were illuminated 
by that blue, I noted again the Place of the Pa- 
per when they caft their Species moft diftincftly 
upon it : And I found that this laft Place of the 
Paper was nearer to the Lens than its former 
Place by about two Inches and an half, or two 
and three quarters. So much fooner therefore 
did the Light in the violet end of the Image 
by a greater Refradion converge and meet, 
than the Light in the red end. But in trying 
this, the Chamber was as dark as I could make 
it. For, if thefe Colours be diluted and weak- 
ned by the Mixture of any adventitious Light, 
the diftance between the Places of the Paper 
will not be fo great. This diftance in the fe- 
cond Experiment, where the Colours of natural 
Bodies were made ufe of, was but an Inch and 
an half, by reafon of the Imperfection of thofe 
Colours. Flere in the Colours of the Prifm, 
which are manifeftly more full, intenfe, and 
lively than thofe of natural Bodies, the diftance 
is two Inches and three quarters. And were the 
Colours ftill more full, I queftion not but that 
the diftance would be confiderably greater. For 
the coloured Light of the Prifm, by the inter- 
fering of the Circles defcribed in the fecond 

Figure 



B O O K L 45 

Figure of the fifth Experiment, and alfo by the 
Light of the very bright Cloiick next the Sun's 
Body intermixing with thefe Colours, and by 
the Light fcattered by the Inequalities in the 
Polifh of the Prifin, was fo very much com- 
pounded, that the Species which thofe faint and 
dark Colours, the indigo and violet, caft upon 
the Paper were not diilind enough to be well ob- 
ferved. 

Exper. g. A Prifm, whofe two Angles at its 
Bafe were equal to one another, and half right 
ones, and the third a right one, I placed in a 
Beam of the Sun's Light let into a dark Cham- 
ber through a Hole in the Window-fhut, as in 
the third Experiment. And turning the Prifin 
flowly. about its Axis, until all the Light which 
went through one of its Angles, and was refradl- 
ed by it began to be refled:ed by its Bafe, at 
which till then it went out of the Glafs, I cb- 
ferved that thofe Rays which had fuifered the 
greateft Pvcfradiion were fooner reflected than 
the refi:. I. conceived therefore, that thofe Ravs 
of the refledled Light, which were mofi: re- 
frangible, did firfl of all by a total Reflexion 
become more copious in that Light than the 
refi:, and that afterwards the refi: alfo, by a total 
Reflexion, became as copious as thefe. To try 
this, I made the refledted Light pafs through 
another Prifm, and being refracted by it to fall 
afterwards upon a Sheet of white Paper placed 
at fome difiance behind it, and there by that 
Refradion to paint the ufual Colours of the 
Prifm. And then caufing the firfi: Prifm to be 
turned about its Axis as above, I obferved that 

when 



4<5 O P T I C K S. 

when thofe Rays, which in this Prifm had fuf- 
fered the greateft Refraction, and appeared of a 
bkie and violet Colour began to be totally re- 
flected, the blue and violet Light on the Paper, 
which was moft refracted in the fecond Prifm, 
received a fenlible Increafe above that of the 
red and yellow, which was leafl refracted ; and 
afterwards, when the reft of the Light which 
was green, yellow, and red, began to be totally 
reflected in the firft Prifm, the Light of thofe 
Colours on the Paper received as great an In- 
creafe as the violet and blue had done before. 
Whence 'tis manifeft, that the Beam of Light 
reflected by the Bafe of the Prifm, being aug- 
mented firft by the more refrangible Rays, and 
afterwards by the lefs refrangible ones, is com- 
pounded of Rays diiferently refrangible. And 
that all fuch reflected Light is of the fame Na- 
ture with the Sun's Light before its Incidence 
on the Bafe of the Prifm, no Man ever doubt- 
ed y it being generally allowed, that Light by 
fuch Reflexions fuffers no Alteration in its Modi- 
fications and Properties. I do not here take No- 
tice of any RefraCtions made in the fides of the 
firft Prifm, becaufe the Light enters it perpendi- 
cularly at the firft fide, and goes out perpendicu- 
larly at the fecond fide, and therefore fuffers 
none. So then, the Sun's incident Light being of 
tlie fame Temper and Conftitution with his emer- 
gent Light, and the laft being compounded of 
Rays differently refrangible, the firft muft be in 
like manner compounded. 

lUuJtratmi. In the twenty-firft Figure, ABC 
is the firft Prifm, B C its Bafe, B and C its 

equal 



B O O K I. 47 

equal Angles at the Bafc, each of 4^ Degrees, 
A its reftangular Vertex, F M a beam of the 
€un's Light let into a dark Room through a 
hole F one third part of an Inch broad, M its 
Incidence on the Bafe of the Prifm, M G a lefs 
refrafted Ray, M H a more refradted Ray, M N 
the beam of Light refleded from the Bafe, 
V X Y the fecond Prifm by which this beam in 
paffing through it is refradled, N t the lefs re- 
fraded Light of this beam, and N/> the more 
refraded part thereof. When the firft Prifm 
A B C is turned about its Axis according to the 
order of the Letters ABC, the Rays MH e- 
merge^more and more obliquely out of that 
Prifm, and at length after their moft oblique 
Emergence are refleded towards N, and going 
on to p do increafe the Number of the Rays 
N^. Afterwards by continuing the Motion of 
the iirft Prifm, the Rays M G are alfo refleded 
to N and increafe the number of the Rays N f. 
And therefore the Light MN admits into its 
Compofition, firft the more refrangible Rays, 
and then the lefs refrangible Rays, and yet af- 
ter this Compofition is of the fame Nature with 
the Sun's immediate Light F M, the Reflexion 
of the fpecular Bafe B C caufing no Alteration 
therein. 

Rxper. 10. Two Prifms, which were alike 
in Shape, I tied fo together, that their Axis and 
oppofite Sides being parallel, they compofed a 
Parallelopiped. x^nd, the Sun finning into my 
dark Chamber through a little hole in the Win- 
dow-fliut , I placed that Parallelopiped in his 
beam at fome diftancc from the hole, in fuch a 

Pofi:urc\ 



O P T I C K S. 

Pofture, that the Axes of the Prifms might be 
perpendicular to the incident Rays , and that 
thole • Rays being incident upon the firft Side 
of one Prifm, might go on through the two 
contiguous Sides of both Prifms, and emerge 
out of the laft Side of the fecond Prifm. This 
Side being parallel to the firft Side of the firfl 
Prifm, caufed the emerging Light to be paral- 
lel to the incident. Then, beyond thefe two 
Prifms I placed a third, which might refrad; 
that emergent Light , and by that Refradiion 
caft the ufual Colours of the Prifm upon the 
oppofite Wall, or upon a fheet of white Paper 
held at a convenient Diftance behind the Prifm 
for that refracCled Light to fall upon it. After 
this I turned the Parallelopiped about its Axis, 
and found that when the contiguous Sides of 
the two Prifms became fo oblique to the inci- 
dent Rays, that thofe Rays began all of them to 
be refled:ed, thofe Rays which in the third 
Prifm had fuffered the greateft Refraction, and 
painted the Paper with violet and blue, were 
firft of all by a total Reflexion taken out of the 
tranfmitted Light , the reft remaining and on 
the Paper painting their Colours of green, yel- 
low, orange and red, as before ; and afterwards 
by continuing the Motion of the two Prifms, 
the reft of the Rays alfo by a total Reflexion 
vanift^ed in order, according to their degrees 
of Refrangibility. The Light therefore which 
emerged out of the two Prifms is compound- 
ed of Rays differently refrangible, feeing the 
more refrangible Rays may be taken out of it, 
while the lefs refrangible remain. But this 

Light 



B O O K I. 4p 

Light being trajeded only through the parallel 
Superficies of the two Prifms, if it fuffer'd any 
change by the Refradlion of one Superficies it 
lofl that Impreihon by the contrary Refraction 
of the other Superficies, and fo being refbor'd to 
its priftine Conftitution, became of the fame Na- 
ture and Condition as at firfl before its Incidence 
on thofe Prifms ; and therefore, before its Inci- 
dence, was as much compounded of Rays diffe- 
rently refrangible, as afterwaVds. 

llliiftration. In the twenty fecond Figure 
ABC and BCD are the two Prifms tied together 
in the form of a Parallelopiped , their Sides 
B C and C B being contiguous, and their Sides 
A B and C D parallel. And H J K is the third 
Prifm, by which the Sun's Light propagated 
through the hole F into the dark Chamber, and 
there pafiing through thofe fides of the Prifms 
AB, BC, CBandCD, is refraded at O to 
the white Paper P T, falling there partly upon 
P by a greater Refra6ticn, partly upon T by a 
lefs Refraction, and partly upon R and other in- 
termediate places by intermediate Ref rations. 
By turning the Parallelopiped A C B D about its 
Axis, according to the order of tlie Letters A, 
C, D, B, at length when the contiguous Planes 
B C and C B become futhciently oblique to the 
Rays F M, which are incident upon them at M, 
there will vanifh totally out of the refraded 
Light OPT, firfl of ail the mofl refraded Rays 
OP, (the reft OR and O T remaining as be- 
fore ) then the Rays O R and other intermedi- 
ate ones, and laftly, the leaft refracted Rays OT- 
For when the Plane BC becomes fufficiently 

E oblique 



50 O P T I C K S. 

oblique to the Rays incident upon it , tliofe 
Rays will begin to be totally refleded by it to- 
wards N J and firft the moft refrangible Rays 
will be totally refledted ( as was explained in 
the preceding Experiment ) and by Confequence 
muft firft difappear at P , and afterwards the 
reft as they are in order totally refledted to N, 
they niuft difappear in the fame order at R 
and T. So then the Rays which at O fuf- 
fer the greatefl Refraftion, may be taken out 
of the Light M O whilft the reft of the Rays 
remain in it , and therefore that Light M O 
is compounded of Rays differently refrangi- 
ble. And becaufe the Planes A B and C D 
are parallel, and therefore by equal and con- 
trary Refradlions deftroy one anothers Ef- 
fects, the incident Light F M muft be of the 
fame Kind and Nature with the emergent Light 
M O, and therefore doth alfo confifl of Rays 
differently refrangible. Thefe two Lights F M 
and M O, before the moft refrangible Rays are 
feparated out of the emergent Light M O, a- 
gree in Colour, and in all other Properties lo 
far as my Obfervation reaches , and therefore 
are defervedly reputed of the fame Nature and 
Conftitution, and by Confequence the one is 
compounded as well as the other. But after 
the moft refrangible Rays begin to be totally 
refledted, and thereby feparated out of the e- 
mergent Light M O, that Light changes its Co- 
lour from white to a dilute and faint yellow, 
a pretty good orange, a very full red fuccef- 
fively, and then totally vanifties. For after the 
moft refrangible Rays which paint the Paper at 
2 P with 



B O O K I. 51 

P with a purple Colour^ are by a total P.efje^ 
xion taken out of the beam of Light M O, the 
reft of the Colours which appear on the Paper 
at R and T being mix'd in the Liglit M O 
compound there a faint yellow, and after the 
blue and part of the green which appear on the 
Paper between P and R are taken away, the reft 
which appear between R and T ( that is the yel- 
low, orange, red and a little green) being mix- 
ed in the beam MO compouiid there an orange; 
and when all the Rays are by Reflexion taken 
out of the beam M O, except: the leaft refran- 
gible, which at T appear of a full red, their 
Colour is the fame in that beam M O as after- 
wards at T, the Refrafticn of the Prifm H J K 
ferving only to feparate the differently refrangible 
Rays, without making any Alteration in their 
Colours, as ftiall be more fully proved hereafter. 
All which confirms as well the firft Propofition 
as the fecond. 

Scholium. If this Experiment and the former 
be conjoined and made one by applying a fourth 
Prifm VX Y [in Fig. 22.] to refra(5t the refied:ed 
beam M N towards //>, the Conclufion will be 
clearer. For then the Light N/> v/hich in the 
fourth Prifm is more refracted,- will become ful- 
ler and ftronger when the Light O P, which in 
the third Prifm H J K is more refracted, va- 
nifties at P; and afterwards when the lefs re- 
fracted Light O T vanifhes at T, the lefs re- 
fraded Light N t will become increafed whilft 
the more refracted Light at p receives no far- 
ther increafe. And as the traje6ted beam M O 
in vanifbing is always of fuch a Colour as ought 



52 o p T I c K s: 

to refult from the mixture of the Colours which 
fall upon the Paper P T , fo is the refleded 
beam M N always of fuch a Colour as ought to 
refult from the mixture of the Colours which 
fall upon the Paper p t. For when the mofl 
refrangible Rays are by a total Reflexion taken 
out of- the beam M O, and leave that beam of 
an orange Colour, the Excefs of thofe Rays in 
the refled:ed Light, does not only make the vio- 
let, indigo and blue at p more full, but alfo 
makes the beam M N change from the yellowidi 
Colour of the Sun's Light, to a pale white in- 
clining to blue, and afterward recover its yel- 
lowifli Colour again, fo foon as all the reft of the 
tranfmitted Light M O T is reflected. 

Now feeing that in all this variety of Expe- 
riments , whether the Trial be made in Light 
refledled, and that either from natural Bodies, 
as in the firft and fecond Experiment, or fpe- 
cular, as in the ninth; or in Light refrad:ed, 
and that either before the unequally refracted 
Rays are by diverging fepa rated from one an- 
other, and loling their whitenefs which they 
have altogether, appear feverally of feveral Co- 
lours, as in the fifth Experiment; or after they 
are feparated from one another, and appear co- 
lour'd as in the fixth, feventh, and eighth Ex- 
periments; or in Light trajedted through paral- 
lel Superficies, deftroying each others Eifedis, 
as in the tenth Experiment ; there are always 
found Rays, which at equal Incidences on the 
fame Medium fufFer unequal Refractions, and 
that without any fplitting or dilating of fmgle 
Rays, or contingence in the inequality of the 
3. Refra- 



B O O K I. 53 

Refradtions, as is proved in the fifth and fixth 
Experiments. And feeing the Rays which dif- 
fer in Refranglbility may be parted and forted 
from one another, and that either by Refradion 
as in the third Experiment, or by Reflexion as in 
the tenth, and then the fcveral forts apart at 
equal Incidences fuffer unequal Refradions, and 
thofe' forts are more refracted than others after 
Separation, which were more refraded before 
it, as in the fixth and following Experiments, 
and if the Sun's Light be trajeded through three 
or more crofs Prifms fucceffively, thofe Rays 
•which in the firft Prilm are refraded more than 
others, are in all the following Prifms refraded 
more than others in the fame Rate and Propor- 
tion, as appears by the fifth Experiment j it's 
manifeft that the Sun's Light is an heterogeneous 
Mixture of Rays, fome of which are conftantly 
more refrangible than others, as was propofed. 



PROP, m. Theor. III. 
'The Suns Light conftjls of PMys differing 
in Reflexibility^ and thofe Puiys are more 
reflexible than others 'which are more 
refra?igible. 

np H I 8 is manifeft by the ninth and tenth 
*■- Experiments : For in the ninth Experi- 
ment, by turning the Prifm about its Axis, un- 
til the Rays within it which in going out into 
the Air were refraded by its Bafe, became fo 
oblique to that Bafe, as to begin to be totally 

E 3 refiede4 



54 O P T I C K S. 

refleded thereby; thofe Rays became iirft of all 
totally refledied, which before at equal Inciden- 
ces with the reft had fuffered the greateft Refra-. 
(Stion. And the fame thing "happens in the Refle- 
xion made by the commDn Bafe of the two 
Prifms in the tenth Experiment. 

PROP. IV. Prob. L 

7v fepa7^ate from one another the heteroge- 
neous Rays of compound Light, 



^"T^ H E heterogeneous Rays are in fome mea- 
-*- fure feparated from one another by the 
Refradion of the Prifm in the third Experi^ 
ment, and in the fifth Experiment, by taking a-r 
way the Penumbra from the redilinear fides of 
the coloured Image, that Separation in thofe ve- 
ry rcdilinear lides or ftraight edges of the I- 
mage becomes perfed. But in all places be- 
tween thofe rectilinear edges, thofe innumera- 
ble Circles there defcribed, which are feveral- 
ly illuminated by homogeneal Rays, by interfe- 
ring with one another, and being every where 
commix'd , do render the Light fufficiently 
compound. But if thefe Circles, whilft their 
Centers keep their Diftances and Pofitions, could 
be made lefs in Diameter, their interfering one 
with another, and by Confequence the Mixture 
of the heterogeneous Rays would be propor- 
tionally diminiih'd. In the twenty third Figure 
let AG, BH, CJ, DK, EL, FM be the Cir- 
cles which fo many forts of Rays flowing frppi 

the 



B O O K I. 55 

the fame dlfque of the Sun, do in the third Ex- 
periment illuminate j of all • which and innu- 
merable other intermediate ones lying in a con- 
tinual Series between the two rectilinear and pa- 
rallel edges of the Sun's oblong Image P T , 
that Image is compos'd, as was explained in 
the fifth Experiment. And let ^^, bh^ ci^ d ky 
e /, fm be fo many lefs Circles lying in a like 
continual Series between two parallel right Lines 
^y and g m with the fame diftances between their 
Centers, and illuminated by the fame forts of 
Rays, that is the Circle a g with the fmie fort 
by which the correfponding Circle A G was il- 
luminated, and the Circle b h with the furie fort 
by which the correfponding Circle B H was illu- 
minated, and the reft of the Circles ci, d k, el, 
fm refped;ively, with the fame forts of Rays by 
which the feveral correfponding Circles C J, 
D K, EL, F M were illuminated. In the Fi- 
gure P T compofed of the greater Circles, three 
of thofe Circles A G, B H, C J, are fo ex- 
panded into one another, that the three forts of 
Rays by which thofe Circles are illuminated , 
together with other innumerable forts of inter- 
mediate Rays, are mixed at Q^^ in the middle of 
the Circle B H. And the like Mixture happens 
throughout almofl the whole length of the Fi- 
gure P T. But in the Figure p t compofed of 
the lefs Circles, the three lefs Circles a g^ b hy c /, 
which anfwer to thofe three greater, do not ex- 
tend into one another j nor are there any v/liere 
mingled fo much as any two of the three forts of 
Rays by which thofe Circles are illuminated, and 

E 4 whicls 



5^ 



O P T I C K S. 



which in the Figure P T are all of them inter- 
mingled at B H. 

Now he that fhall thus conlider It, will eafily 
underfland that the Mixture is diminifhed in 
the fame Proportion with the Diameters of the 
Circles. If the Diameters of the Circles whilil . 
their Centers remain the fame, be made three 
times lefs than before, the Mixture will be alfo 
three times lefs; if ten times lefs, the Mixture 
will be ten times lefs, and fo of other Propor- 
tions. That is, the Mixture of the Rays in the 
greater Figure P T will be to their Mixture in 
the lefs/>/, as the Latitude of the greater Fi- 
gure is to the Latitude of the lefs. For the La- 
titudes of thefe Figures are equal to the Dia- 
meters of their Circles. And iience it eafily fol- 
lows, that the Mixture of the Rays in the re- 
'fra(fted Spedlrum pt is to the Mixture of the 
Rays in the dired: and immediate Light of the 
Sun, as the breadth of that Spedrum is to the 
difference between the length and breadth of the 
fame Specflrum. 

So then, if we would diminifh the Mixture 
of the Rays, we are to diminifli the Diameters 
of the Circles. Now thefe would be diminifh- 
ed if the Sun's Diameter to which they anfwer 
could be made lefs than it is, or ( which comes 
to the fame Purpofe) if without Doors, at a 
great diflance from the Prifm towards the Sun, 
fom.e opake Body were placed, with a round 
iioje in the middle of it , to intercept ail the 
Sun's Light , excepting fo much as coming 
from the middle of his Body could pafs through 

that 



BOOK! 57 

that Hole to the Prifm. For fo the Circles A G, 
B H, and the reft, would not any longer anfwer 
to the whole Difque of the Sun, but only to that 
Part of it which could be feen from the Prifm 
through that Hole, that it is to the apparent Mag- 
nitude of that Hole view'd from the Prifm. But 
that thefe Circles may anfwer more diftindtly to 
that Hole, a Lens is to be placed by the Prifm to 
cafl the Image of the Hole, (that is, every one 
of the Circles AG, BH, &c.) . diflindly upon 
the Paper at PT, after fuch a manner, as by a 
Lens placed at a Windovy% the Species of Ob- 
jects abroad are caft diftindtly upon a Paper 
within the Room, and the red:ilinear Sides of 
the oblong Solar Image in the fifth Experiment 
became diilind: without any Penum.bra. If this 
be done, it will not be neceflary to place that 
Hole very far off, no not beyond the Win- 
dow. And therefore inftead of that Hole, I 
ufed the Hole in the Window-lluit, as fol- 
lows. 

Expcr. II. In the Sun's Light let into my 
darken'd Chamber through a fmall round Hole 
in my Window-fluit, at about ten or twelve 
Feet from the Window, I placed a I^ens, by 
which the Image of the Hole might be diilindly 
call upon a Sheet of white Paper, placed at 
the diftance of fix, eight, ten, or twelve Feet 
from the Lens. For, according to the diffe* 
rence of the Lenfes I ufed various diftances, 
which I think not worth the while to defcribe. 
Then immediately after the Lens I placed a 
Prifm, by which the trajeded Light might be 
refracted either upwards or fide-ways, and there- 

' by 



y8 O P T I C K S. 

by the round Image, which the Lens alone did 
caft upon the Paper might be drawn out into a 
long one with Parallel Sides, as in the third Ex- 
periment. This oblong Image I let fall upon 
another Paper at about the fame diftance from 
the Prifm as before, moving the Paper either 
towards the Prifm or from it, until I found the 
juil diftance where the Redilinear Sides of the 
Image became moft diflind:. For in this Cafe, 
theCircular Images of the Hole, which compofe 
that Image after the fame manner, that the Cir- 
cles ag^ bh^ ci^ &c. do the Figure ^/ [in Fig.21^ 
were terminated moft diftindly without any 
Penumbra, and therefore' extended into one ano- 
ther the leaft that they could, and by confequence 
the Mixture of the heterogeneous Rays was now 
the leaft of all. By this means I ufed to form 
an oblong Image (fuch as is p t) [in Fig. 23, 
and 24.] of Circular Images of the Hole, (fuch 
as are agy bh, ciy &;c.) and by ufmg a greater 
or^lefs Hole in the Window-fhut, I made the 
Circular Images a g, b hy ciy Sec. of which it 
was formed, to become greater or lefs at pleafure, 
and thereby the Mixture of the Rays in the 
Image p t to be as much, or as little as I de- 
fired. 

IlluJlratio7i. In the tu'enty-fourth Figure, F 
reprefents the Circular Hole in the Window- 
fhut, MN the Lens, whereby the Image or Spe- 
cies of that Hole is caft diftindly upon a Paper 
at J, ABC the Prifm, whereby the Rays are at 
their emerging out of the Lens refrafted from. 
J towards another Paper at p /, and the round 
Image at J is turned into an oblong Image pt 

falling 



B O O K I. s-p 

falling on that other Paper. This Image // con- 
lifts of Circles placed one after another in a Recti- 
linear Order, as was fufficiently cxplaii^^ed in the 
fifth Experiment j and thefe Circles are equal to 
the Circle J, and confequently anfwer in magni- 
tude to the Hole F^ and therefore by diminifhing 
that Hole they may be at pleafure diminiihed, 
whilft their Centers remain in their Places. By 
this means I made the Breadth of the Image p t 
to be forty times, and fometimes fixty or feventy 
times lefs than its Length. As for inflance, if 
tlie Breadth of the Hole F be one tenth of an 
Inch, and MF the diflance of the Lens from the 
Hole be 12 Feet; and \i pV> or pM the diftance 
of the Image pi from the Prifm or Lens be 10 
Feet, and the refracting Angle of the Prifm be 
62 Degrees, the Breadth of the Image pt will 
be one twelfth of an Inch, and the Length about 
iix Inches, and therefore the Length to the 
Breadth as 72 to i, and by confequence the 
Light of this Image 71 times lefs compound 
than the Sun's dired: Light. And Light thus far 
iimple and homogeneal, is fufficient for trying 
all the Experiments in this Book about fimple 
Light. For the Compofition of heterogeneal 
Rays is in this Light fo little, that it is fcarce to 
be difcovered and perceiv'd by Senfe, except per- 
haps in the indigo and violet. For thefe being 
dark Colours, do eafily fuffer a fenfible Allay 
by that little fcattcring Light which ufes to be 
refraded irregularly by the Inequalities of the 
Prifm. 

Yet inftead of the Circular Llole F, 'tis better 
to fubftitute an oblong Hole iliaped like a long 

Paral- 



6o O P T I C K S. 

Parallelogram with its Length parallel to the 
Prifm ABC. For if this Hole be an Inch or 
two long, • and but a tenth or twentieth Part of an 
Inch broad, or narrower j the Light of the Image 
ft will be as fimple as before, or fimpler, and 
the Image will become much broader, and there- 
fore more fit to have Experiinents try'd in its 
Lisht than before. 

Inftead of this Parallelogram Hole may be fub- 
ftituted a triangular one of equal Sides, whofe 
Bafe, for inftance, is about the tenth Part of an 
Inch, and its Height an Inch or more. For by 
this means, if the Axis of the Prifm be parallel to 
the Perpendicular of the Triangle, the Image />^ 
[in Fig. 25.] will now be form'd of equicrural 
Triangles ^o-j bh^ ci, dk^ el,f?ji, &c. and in- 
numerable other intermediate ones anfwering to 
the triangular Hole in Shape and Bignefs, and lying 
one after another in a continual Series between 
two Parallel Lines ^y^and gm. Thefe Triangles, 
are a little intermingled at their Bafes, but not at 
their Vertices ; and therefore the Light on the 
brighter Side af of the Image, where the Bafes 
of the Triangles are, is a little compounded, but 
on the darker Side gm \% altogether uncom- 
pounded, and in all Places between the Sides the 
Compofition is proportional to the diftances of 
the Places from that obfcurer Side gm. And ha-? 
ving a Spedrum pt oi fuch a Compofition, we 
m.ay try Experiments either in its fcronger and lefs 
fimple Light near the Side af^ or in its weaker and 
fimpler Light near the other Side gm, as. it fhall 
feem mofl convenient. 



But 



B O O K L 6 1 

But ill making Experiments of this kind, the 
Chamber ought to be made as dark as can be, 
left any Foreign Light mingle it felf with the 
Light of the Spedrum p t^ and render it com- 
pound J efpecially if we would try Experiments 
in the more fmiple Light next the Side g m of 
the Spectrum J which being fainter, will have 
a lefs proportion to the Foreign Light ; and fo 
• by the mixture of that Light be more troubled, 
and made more compound. The Lens alfo 
ought to be good, fuch as may ferve for opti- 
cal Ufes, and the Prifm ought to have a large 
Angle, fuppofe of 65 or 70 Degrees, and to be 
well wrought, being made of Glafs free from 
Bubbles and Veins, with its Sides not a little 
convex or concave, as ufually happens, but truly 
plane, and its Polifli elaborate, as in working 
Optick-glalTes, and not fuch as is ufually wrought 
with Putty, whereby the edges of the Sand- 
holes being worn away, there are left all over 
the Glafs a numberlefs Company of very little 
convex polite Rifings like Waves. The edges 
alfo of the Prifm and Lens, fo far as they may 
make any irregular Refraftion, muft be covered 
with 2l black Paper glewed on. ilad all the 
Light of the Sun's-Beam let into the Chamber, 
which is ufelefs and unprofitable to the Experi- 
ment, ought to be intercepted v/ith black Pa- 
per, or other bkck Obftacles. For otherwife 
the ufelefs Light being refled:ed every way in 
the Chamber, will mix with the oblong Spe- 
ctrum, and help to difturb it. In trying thefe 
Things, fo much diligence is not altogether ne- 
celiary, but it will promote tlie Succefs of the 

Expe- 



6i O P T I C K S. 

Experiments, and by a veiy fcrupulous Examiner 
of Things deferves to be apply'd. It's difficult 
to get Glafs Prifms lit for riiis Purpofe, and there- 
fore I ufed fometimes prifmatick VelTels made 
with pieces of broken Looking-glaffes, and filled 
with Rain Water. And to increafe the Refradion, 
I fometimes impregnated the Water ftrongly with 
Saccharum Saturni, 



PROP. V. Theor. IV. 

Homogeneal Light is refraSied regularly 
^without any D Hat atio7if putting or Jhatter^ 
ing of the Rays ^ a7id the co?if ufed Vijion of 
ObjeBs feen through refraEiing Bodies by 
heteroge7ieal Light arifes from the diffe-^ 
rent Refrangibility of fever al forts of Rays, 

TH E firft Part of this Propofition has been 
already fufficiently proved in the fifth Ex- 
periment, and will farther appear by the Experi- 
ments which follow. 

Exper. 12. In the middle of a black Paper I 
made a round Hole about a fifth or fixth Part of 
an Inch in diameter. Upon this Paper I caufed 
the Spedrum of homogeneal Light defcribed 
in the former Propofition, fo to fall, that fome 
part of the Light m.ight pafs through the Hole 
of the Paper. This tranfmitted part of the 
Light I refrafted with a Prifm placed behind 
^he Paper, and letting this refracted Light fall 
perpendicularly upon a white Paper two or 
three Feet diftant from the Prifm, 1 found that 

the 



B O O K I. 63 

the Spe6trum formed on the Paper by this Light 
was not oblong, as when 'tis made ( in the third 
Experiment) by refra-fling the Sun's compound 
Light, but was (fo far as I could judge by my 
Eye ) perfedily circular, the Length being no 
greater than the Breadtl 1. Which fhev/s, that this 
Light is refracted regularly without any Dilatation 
of the Rays. 

Exper. 13. In the homogeneal Light I placed 
a Paper Circle of a quarter of an Lich in diameter, 
and in the Sun's unrefra6ted heterogeneal white 
Light I placed another Paper Circle of the fame 
Bignefs. And going from the Papers to the di- 
ftance of fomeFeet, I viewed both Circles through 
a Prifm. The Circle illuminated by the Sun's he- 
terogeneal Light appeared very oblong, as in the 
fourth Experiment, the Length being many times 
greater than the Breadth j but the other Circle, 
illuminated with homogeneal Light, appeared cir- 
(iular and diftindtly defined, as when 'tis view'd 
with the naked Eye. Which proves the whole Pro- 
pofition. 

Exper. 14. In the homogeneal Light I placed 
Flies, and fuch-like minute Objedls, and view- 
ing them through a Prifm, I faw their Parts as 
diftindlly defined, as if I had viewed them with 
the naked Eye. The fame Objed:s placed in 
the Sun's unrefradted hetero2;eneal Lig-ht, which 
was white, I viewed alio through a Prifm, and 
faw them rnoxl confufcdly defined, fo that I 
could not diftinguiili their fmaller Parts from 
one another. I placed alfo the Letters of a 
fmall print, one while in the homogeneal Light, 
and then in the heterogeneal, and viewing them 

through 



^4 O P T I C K S. 

through a Prifm, they appeared in the latter Cafe 
fo confufed and indiftin^t, that I could not read 
them J but in the former they appeared fo diftindt, 
that I could read readily, and thought I faw them 
as diflind:, as when I view'd them with my naked 
Eye. In both Cafes I view'd the fame Objeds, 
through the fame Prifm at the fame diftance from 
me, and in the fame Situation. There was no 
difference, but in the Light by which the Objedts 
were illuminated, and which in one Cafe was 
iimple, and in the other compound ; and there- 
fore, the diftindl Vifion in the former Cafe, and 
confufed in the latter, could arife from nothing 
elfe than from that difference of the Lights. 
Which proves the whole Propofition. 

And in thefe three Experiments it is farther 
very remarkable, that the Colour of homogeneal 
Light w^as never changed by the Refrad:ion. 



PROP. VL Theor. V. 

T'he Sine of Incidence of every Ray confi- 
dered apart ^ is to its Sine of RefraEiion 
i7i a given Ratio, 

THAT every Ray confider'd apart. Is con- 
ftant to it felf in fome degree of Refran- 
gibility, is fufficiently manifeft out of what has 
been faid. Thofe Rays, which in the firfh Re- 
fra(5tion, are at equal Incidences moll refraded, 
are alfo in the following Refradions at equal 

Inci- 



BOOK!. S^ 

Incidences moft refracted ; and fo of the leaft 
refrangible, and the reft which have any mean 
Degree of Refrangibility, as is manifeft by the 
fifth, fixth, feventh, eighth, and ninth Expe- 
riments. And thofe which the firft Tiilie at 
like Incidences are equally refraded, are again 
at like Incidences equally and uniformly retract- 
ed, and that whether they be refraded before 
they be feparated from one another, as in the 
fifth Expernnent, or whether they be refradted 
apart, as in the twelfth, thirteenth and four- 
teenth Experiments. The Refraction therefore 
of every Ray apart is regular, and what Rule that 
Refradiion obferves we are now to (liew*. 

The late Writers in Opticks teach, that the 
Sines of Incidence are in a given Proportion 
to the Sines of Refradion, as was explained in 
the fifth Axiom ; and fome by Inllruments fit- 
ted for meafuring of Refractions, or otherwife 
experimentally examining this Proportion, do 
acquaint us that they have found it accurate. 
But whilft they, not underftanding the difife- 
rent Refrangibility of feveral Rays, conceived 
them all to be refraCted according to one and 
the fame Proportion, 'tis to be prefumed that 
they adapted their Meafures only to the middle 
of the refracted Light ; fo that from their Mea- 
fures we may conclude only that the R^iys 
which have a mean Degree of Refrangibility, 
that is, thofe which when feparated from the 
reft appear green, are refraCted according to a 
given Proportion ,of their Sines. And there- 

* This is •venfulh treated of in our Author'/ Left. Optic Part \, 
Seil.lL 

F fore 



6& O F T I C K S. 

fore we are now to fhew, that the like given 
Proportions obtain in all the reft. That it 
fhould be fo is very reafonable, Nature being 
ever conformable to her felf -, but an experimen- 
tal Proof is defired. And fuch a Proof will be had, 
if we can fliew that the Sines of Refradion of 
Rays differently refrangible are one to another ia 
a given Proportion when their Sines of Incidence 
are equal. For, if the Sines of Refraction of all 
the Rays are in given Proportions to the Sine of 
Refractions of a Ray which has a mean Degree of 
Refrangibility, and this Sine is in a given Propor- 
, tion to the equal Sines of Incidence, thofe other 
Sines of Refradtion will alfo be in given Propor- 
tions to the equal Sines of Incidence. Now, 
when the Sines of Incidence are equal, it will 
appear by the following Experiment, that the 
Sines of Refradion are in a given Proportion tQ 
one another. 

Exper. 15. The Sun fhining into a dark Cham- 
ber through a little round Hole in the Window- 
fhut, let S [in Fig. 26.] reprefent his round 
white Image painted on the oppofite Wall by 
his dired: Light, P T his oblong coloured 
Image made by refrading that Light with a 
Prifm placed at the Window -, and p t, or 
2p 2.t^ or 3/> 3 Z', his oblong colour'd Image 
made by refrading again the fame Light fide- 
ways with a fecond Prilm placed immediately 
after the firft in a crofs Pontion to it, as was 
explained in the fifth Experiment j that is to 
fay, p t when the Refradion of the fecond 
Prifm is fmall, zp 2 t when its Refracftion is 
greater, and 3 /> 3 ^ when it is greateft. For 

fuch 



B O O K I. 6j 

fuch will be the diverfity of the Pvefradions, if 
the refrading Angle of the fecond Prifm be of 
various Magnitudes 3 fuppofc of fifteen or twen- 
ty Degrees to make the Image pt^ of thirty or 
forty to make the Image 2p 2t^ and of fixty to 
make the Image 3/> 3/. But for want of folid 
Glafs Prifms with Angles of convenient Big- 
neffes, there may be Veffels made of poliflied 
Plates of Glafs cemented together in the form of 
Prifms and filled with Water. Thefe things be- 
ing thus ordered, I obferved that all the folar 
Images or coloured Spectrums P T , />/ , 2p 
2.ty 3/> 3^ did very nearly converge to the place 
S on which the dired Light of the Sun fell 
and painted his white round Image when the 
Prifms were taken away. The Axis of the Spe- 
ctrum PT, that is the Line drawn through the 
middle of it parallel to its re(5tilinear Sides , 
did when produced pafs exadtly through the 
middle of that white round Image S. And when 
the RefracStion of the fecond Prifm \t^s equal 
to the Refradion of the firfi:, the refrading An* 
gles of them both being about 60 Degrees, the 
Axis of the Spectrum 3/^3^ made by that Re- 
fraction, did when produced pafs alfo throuo-h 
the middle of' the fame white round Imao-e S. 
But when the Refraction of the fecond Prifm 
was lefs than that of the firft, the produced 
Axes of the SpeClrums tp or 2t 2p made by 
that Refraction did cut the produced A^xis of 
the Spectrum TP in the points m and fi, a lit- 
tle beyond the Center of that white round I- 
mage S. Whence the proportion of the Line 
3/ T to the Line 3/>P was a little greater than 

F 2 the 



6% O P T I C K S. 

d^e Proportion of 2/T to 2/>P, and this Pro- 
portion a little greater than that of iT to p P. 
Now -^vhefi the Light of the Spedtrum P T falls 
perpendicularly upon the Wall , thofe Lines 
3 4fT, 3/»P, and2^T, 2/P, and ^T, /P, are 
the Tangents of the Refra<5tions, and therefore 
hy this Experiment the Proportions of the Tan-- 
gents of the Refradions are obtained , from 
whence the Proportions of the Sines being de- 
rived, they come out equal, fo far as by view- 
ing the SpeftrumSj and ufing fome mathemati- 
cal R^albiiing i could eftimate. For I did not 
irtaJic an accurate Computation. So then the 
Propolition holds true in every Ray apart, fo 
hr as appears by Experiment. And that it is 
accurately true, may be demonftrated upon this 
Suppolition. 1'hat Bodies refi-a^ Light by a5fing 
zipoti its Rays in Li?i€s perpmdicular to their Sur^ 
faces. But in order to this Demonftration, I muil 
diftinguifh the Motion of every Ray into two 
Motions, the one perpendicular to the refradiing 
Surface, the other parallel to it, and concerning 
the perpendicular Motion lay down the follow- 
ing Propolition. 

If any Motion or moving thing whatfoever he 
incident with any Velocity on any broad and 
thin fpace terminated on both fides by two paral- 
lel Planes , and in its Paffage through that 
fpace be urged perpendicularly towards the far- 
ther Plane by any force which at given diftances 
fi-om the Plane is of given Quantities ; the per- 
pendicular velocity of that Motion or Thing, 
at is emerging out of that fpace, fhall be always 
equal to the fquare Root of the funi of the 
3 . fquare 



B O O K I. 69 

fquare of the perpendicular velocit}^ of xki'iX 
Motion or Thing at its Incidence on that fpace^ 
and of the fquare of the perpendicular velocity 
wliich that Motion or Tiling would have at its 
Emergence, if at its Incidence its perpendicular 
velocity '^vas infinitely little. 

And' the fame Propofition holds true of any 
Motion or Thing perpendicul^ly retarded in its 
paffage through that Ipace, if inilead of the iura 
of the two Squares you take their ditference;. 
The Demonflration Mathematicians v*ill eafily 
find out, and therefore I iliall not trouble the 
Reader with it. 

Suppofe now that a Ray coming mod oblique- 
ly in the LineMC [in Fig. i.] be refradted at 
C by the Plane RS into the Line CN, and.jf 
it be required to find the Line CE, into which 
any other Ray AC fliall be refradjed ; let MC, 
AD, be the Sines of Incidence of the two Rays, 
and NG, EF, their Sines -of Refradion, and 
let the equal Motions of the incident Rays be 
reprcfented by the equal Lines MC and AC, 
and the Motion M C being confidered as parai^ 
lei to the refracting Plane, let the other Motion 
AC be diflinguiflied into two Motions AD 
and DC, one of which AD is parallel, and tlie 
other DC perpendicular to the refracfting Sur- 
face. In like manner, let the Motions of the 
emerging Rays be diftinguifh'd into two, whereof 

the perpendicular ones are -^ CG and ^ CF. 

And if the force of the refracting Plane begins 
to a<ft upon the Rays either in that Plane or at 
a Certain diftance from it on the one fide, and 
ends ^t a certain diftance from it on the other 

F 3 Side 



^o OPTIC K s. 

fide, and in all places between .thofe two limits 
ad:« upoa the Rays in Lines perpendicular to 
that refrading Plane, and the Actions upon the 
Rays at equal diftances from the refrading Plane 
be equal, and at unequal ones either equal or un- 
equal according to any rate whatever j that Mo- 
tion of the Ray which is parallel to the re- 
frading Plane, will fuffer no Alteration by that 
Fopce 5 and that Motion which is perpendicular 
to it will be altered according to the rule of the 
foregoing Proportion. If therefore for the per- 
pendicular velocity of the emerging Ray C N 

you write -^^ CG as above, then the perpendi- 
cular velocity of any other emerging Ray CE 
which was -^-^CF, will be equal to the fquarc 

Root of CD^ -h f§^ CGq. And by fquaring 

thefe Equals, and adding to them the Equals 
AD^ and MC^ — CD^, and dividing the 
Sums by the Equals CF^-f-EF^ and CG^-f- 

NG^', you will have ~-^ equal to jf^- Whence 

to, the Sine of Incidence, is to E F the Sine of 
efradion, as MC to NG, that is, in a given 
ratio. And this Demonftration being general, 
without determining what Light is, or by what 
kind of Force i: is refraded, or alTuming any 
thing farther than that the refrading Body ada 
upon the Rays in Lines perpendicular to its Sur-. 
face J I take it to be a very convincing Argument 
of the full truth of this Propoiition, 

So then, if the ratio of the Sines of Inci- 
dence and Refradion of any fort of Rays be 

found 



BOOK I. 7.1 

' found in any one cafe, 'tis given in all cafes; and 
this may be readily found by the Method in the 
following Propofition. 

PROP, VII. Theor. VI. 
^he PerfeEiion of Telef copes is hnpeded by 
the different Refrangibilitj of the Rays 
of Light. 

THE Imperfedtion of Telefcopes is vul- 
garly attributed to the fpherical Figures of 
the Glaffes, and therefore Mathematicians have 
propounded to figure them by the conical Sedi- 
ons. To fhew that they are miftaken, I have in- 
ferted this Propofition ; the truth of which will 
appear by the nieafure of the Refractions of the 
feveral forts of Rays ; and thefe meafures I thus 
determine. 

In the third Experiment of this firft Part, 
.where the refracting Angle of the Prifm was 62^ 
Degrees, the half of that Angle 31 deg. 15 min. 
is the Angle of Incidence of the Rays at their go- 
ing out of the Glafs into the Air * ; and the Sine of 
this Angle is 5 188, the Radius being loooo. When 
the Axis of this Ptifm was parallel to the Horizon, 
and the Refraction of the Rays at their Incidence 
6n this Prifm equal to that at their Emergence out 
of it, I obferved v/ith a Quadrant the Angle which 
the mean refrangible P ays, ( that is thofe which 
went to the middle of the Sun's coloured Image ) 
made with the Horizon, and by this Angle and the 
Sun's altitude obferved at the fame time, I found the 

• Seesur AxiXhox's Left. Optic. Parti. Sed. II. §. 29. 

F 4 Angle 



7x O P T I C K S. 

Angle which the emergent Rays contained with the 
incident to be 44 deg. and 40 min. and the half of 
this Angle added to the Angle of Incidence 3 1 deg. 
15 min. makes the Angle of Refracflion, which is 
therefore 5 3 deg. 35 min. and its Sine 8047. Thefe 
are the Sines of Incidence and Refradtion of the 
m^an refrangible Rays, and their Proportion in 
round Numbers is 20 to 3 1. This Glafs was of a 
Colour inclining to green. The laft of the Prifms 
mentioned in the third Experiment was of clear 
white Glafs. Its refracting Angle 635 Degrees. 
The Angle which the emergent Rays contained, 
with the incident 45 deg. 50 min. The Sine of 
half the firft Angle 5262. The Sine of half the 
Sum of the Angles 8157. ^^^^ their Proportion in 
round Numbers 2a to 3 1, as before. 

From the Length of the Image, which was 
about 95 or 10 Inches, fubdud its Breadth, which 
was 2s Inches, and the Rerhainder 71 Inches 
would be the Length of the Image were the Sun 
but a Point, and therefore fubtends the Angle 
which the moft and leafl refrangible Rays, when 
incident on the Prifm in the fame Lines, do 

.'contain with one another after their Emergence. 
"Whence this x^^ngle is 2 deg. o'. f. For, the 

^^if^ance between the Image and the Prifm 
where this Angle is made, was iSj- Feet, and 
at that diftance the Chord 7^ Inches fubtends 
an Angle of 2 deg. o'. y". Now half this Angle 
is the Angle which thefe emergent Rays con- 

' taiH with the emergent mean refrangible Rays, 
and a quarter thereof, that is 30'. 2". may be 
accounted the Angle which they would contain 
with the fame emergent mean refrangible Rays, 

were 



B O OK I. 73 

were they co-incident to them within the Clafs, 
and fuffered no other Refraction than that at.their 
Emergence. For, if two equal Refractions, the 
one at the Incidence of the Rays on the Prifm, 
the other at their Emergence, make half the 
Angle 2 deg. o'. 7''. then one of thofe RefraCtions 
will make about a quarter of that Angle, and this 
quarter added to, and fubduded from the Angle 
of Refraction of the mean refrangible Rays, 
which was 53 deg. 35', gives the Angles of Re- 
fraCtion of the moft and leaft refrangible Rays 
54 deg. 5' 2", and 53 deg. 4' 58", whofe Sines 
are 8099 and 7995, the common Angle of In- 
cidence being 31 deg. 15', and its Sine 5188; 
and thefe Sines in the leafl round Numbers are in 
proportion to one another, as 78 and 'jj to 50. 

Now, if you fubduCt the common Sine of In- 
cidence 50 from the Sines of RefraCtion 'jy and 
78, the Remainders 27 and 28 fliew, that in fmall 
Refractions the RefraCtion of the leafl refrangi- 
ble Rays is to the Refraction of the moft refran- 
gible ones, as 27 to 28 very nearly, and that the 
difference of the RefraCtions of the leafl refran- 
gible and mofl refrangible Rays is about the 
27kh Part of the whole RefraCtion of the mean 
refrangible Rays. 

Whence they that are skilled in Opticks.will 
eafily underfland, *' that the Breadth of the leafl 
circular Space, into which ObjeCt-glaffes of Te- 
lefcopes can colleCt all forts of Parallel Rays, is 
about the 27^th Part of half the Aperture of the 
Glafs, or 55 th Part of the whole Aperture ; and 

* This is demonfi rated in our AuihoiV Led. Optic. Part I. SeSI. IV. 
Fyp. 57. 

that 



74 O P T I C K a 

that the Focus of the moft refrangible Rays is 
nearer to the Objeft-glafs than the Focus of the 
leaft refrangible ones, by about the 275th Part of 
the diflance between the Objed:-glafs and the 
Focus of the mean refrangible ones. 

And if Rays of all forts, flowing from any 
one lucid Point in the Axis of any convex Lens, 
be made by the Refra(3:ion of the Lens to con- 
verge to Points not too remote from the Lens, 
the Focus of the mofl: refrangible Rays fliall be 
nearer to the Lens than the Focus of the leaft 
refrangible ones, by a diflance which is to the 
275th Part of the diftpnce of the Focus of the 
mean refrangible Rays from the Lens, as the di- 
ftance between thrt Focus and the lucid Point, 
from whence the Rays flow, is to the diflance be- 
tween that lucid Point and the Lens very nearly. 

Now to examine whether the Difference be- 
tween the Refra([lions, v^hich the mofl refrangi- 
ble and the leaft refrangible Rays flowing from 
the fame Point fuffer in the Objed-glafTes of Te- 
lefcopes and fuch-like Glafles, be fo great as is 
here defcribed, I contrived the following Experi- 
ment. • 

Exper. 16. The Lens which I ufed in the fe- 
cond and eighth Experiments, being placed fix 
Feet and an Inch diflant from any Obje6t, col- 
leifled the Species of that Objed: by the mean 
refrangible Rays at the diflance of fix Feet and 
an Inch from the Lens on the other fide. And 
therefore by the foregoing P-ule, it ought to col- 
led the Species of that Objedl by the leafl re- 
frangible Rays at the diftance of fix Feet and 
31 Inches from the Lens, and by the mofl re- 
• -' frangible 



BOOK! 75 

frangible ones at the diftance of five Feet and 
iQi Inches from it: So that between the two 
Places, where thefe lead and moft refrangible 
Rays colledl the Species, there may be the di- 
ftance of about 5^ Inches. For by that Rule, 
as fix Feet and an Inch (the diftance of the Lens 
from the lucid Obje6t) is to twelve Feet and 
two Inches ( the diflance of the lucid Objedt 
from the Focus of the mean refrangible Rays ) 
that is, as One is to Two; fo is the 27ith Part 
of fix Feet and an Inch '(the diftance between 
the Lens and the fame Focus) to the diftance 
between the Focus of the moft refrangible Rays 
and the Focus of the leaft refrangible ones, 
which is therefore 5g Inches, that is very nearly 
5^ Inches. Now to know whether this Meafure 
was true, I repeated the fecond and eighth Ex- 
pariment with coloured Light, which was lefs 
compounded than that I there made life of: 
For I now feparated the heterogeneous Rays 
from one another by the Method I defcribed 
in the eleventh Experiment, fo as to make a 
coloured SpecStrum about twelve or fifte^sn Times 
longer than broad. This Spectrum I caft on a 
printed Book, and placing the above-mentioned 
Lens at the diftance of lix Feet and an Inch 
from this Spectrum to colleft the Species of 
the illuminated Letters at the fame diftance on 
the other lidey I found that the Species of the 
Letters illuminated with blue were nearer to 
the Lens than thole illuminated with deep 
red by about three Inches, or three and a quar- 
ter ; but the Species of the Letters illumi- 
nated with indigo and violet appeared fo con- 
I fufed 



75 O P T I C K S. 

fufed and indiftindt, that I could not read them : 
Whereupon viewing the Prifm, I found it was 
s^ full of Veins running from one end of the Glafs 
to the other j fo that the Refradion could not 
be regular. I took another Prifm therefore 
which was free from Veins, and inftead of the 
Letters I ufed two or three Parallel black Lines 
a little broader than the Strokes of the Let- 
ters, and calling the Colours upon thefe Lines 
in fuch manner, that the Lines ran along the 
Colours from one end of the Spedrum to the 
other, I found that the Focus where the indigo, 
or confine of this Colour and violet caft the 
Species of the black Lines mofl diilindly, to 
be about four Inches, or 4^ nearer to the Lens 
than the Focus, where the deepefl red caft the 
Species of th^ fame black Lines mofl diilind:- 
ly. The violet was fo faint and dark, that I 
could not difcern the Species of the Lines di- 
ilindly by that Colour j and therefore confi- 
dering that the Prifm was made of a dark co- 
loured Glafs inclining to green, I took another 
Prifm of clear white Glafs ; but the Spedrum 
of Colours which this Prifm made had long 
white Streams of faint Light (liooting out from 
both ends of the Colours, which made me con- 
clude that fomething w'as amifs j and viewing 
the Prifm, I found two or three little Bubbles 
ja the Glafs, which refraded the Light irregu- 
lar! v. Wherefore I covered that Part of the Glafs 
with black Paper, and letting the Light pafs 
throucrh another Part of it which was free from 
fuch Bubbles, the Spedrum of Colours became 
free from thofe irregular Streams of Light, and, 

was 



B o o k: I. >7 

was now fuch as I defircd. But ftill^I found 
the violet fo dark and faint, that I could fcarce 
fee the Species of the Lines by the violet, and* 
not at all by the deepeft Part of it, which was 
next the end of the Spc,(5lrum. I fufpeded there- 
fore, that this faint and dark Colour might be 
allayed by that fcattering Light which was re- 
fraded, and refleded irregularly, partly by fome 
very fmall Bubbles in the GlafTes, and partly 
by the Inequalities of their Polifh ; which 
Light, tho' it was but little, yet it being of a 
white Colour, might fuffice to affed the Senfe 
fo ftrongly as to difturb the Phaenomena of that 
weak and dark Colour the violet, and there- 
fore I tried, as in the 12th, 13th, and 14th Ex- 
periments, whether the Light of this Colour 
did not confifl of a fenfible Mixture of heteroge- 
neous Rays, but found it did not. Nor did the 
Refradlions caufe any other fenfible Colour than 
violet to emerge ©ut of this Light, as they 
would have done out of white Light, and by 
confequence out of this violet Light had it been 
fenlibly compounded with white Light. And 
therefore I concluded, that the reafon why I 
could not fee the Species of the Lines diftindly 
by this Colour, was only the Darknefs of this 
Colour, and Thinnefs of its Light, and its di- 
ftance from the Axis of the Lens j I divided 
therefore thofe Parallel black Lines into equal 
Parts, by which I might readily know the di- 
ftances of the Colours in the Speftrum from 
one another, and noted the diftances of the 
Lens from the Foci of fuch Colours, as c<ift the . 
Species of the Lines dillindtly, and then confi- 

dered 



'7& O P T I C K S. 

dered vvlaether the difference of thofe distances 
bear fuch proportion to 5| Inches, the greatefl 
Difference of the diftances, which the Foci of 
the deepefl red and violet ought to have from 
the Lens, as the diflance of the obferved Co- 
lours from one another in the Speftrum bear to 
the greatefl diflance of the deepeft red and 
violet meafured in the Redilinear Sides of the 
Spedrum, that is, to the Length of thofe Sides, 
or Excefs of the Length of the Spedrum above 
its Breadth. And my Obfervations were as fol- 
lows. 

When I obferved and compared the deepefl 
fenfible red, and the Colour in the Confine of 
green and blue, which at the Redilinear Sides 
of the Spedirum was diftant from it half the 
Length of thofe Sides, the Focus where the Con- 
fine of green and blue cafl the Species of the 
Lines diflindly on the Paper, was nearer to the 
Lens than the Focus, where the red cafl thofe 
Lines diflind:ly on it by about 25 or 2~ Liches. 
For fometimes the Meafures were a Jittle greater, 
fometimes a little lefs, but feldom varied from 
one another above \ of an Inch. For it was very 
difficult to define the Places of the Foci, with- 
out fome little Errors. Now, if the Colours 
diflant half the Length of the Image, ( mea- 
fured at its Rectilinear Sides) give 25 or 2| Diffe- 
rence of the diflances of their Foci from the 
Lens, then the Colours dillant the whole Length 
ought to give 5 or 55 Inches difference of thofe 
diflances. 

Bpt here it's to be noted, that I could not 
fee the red to the full end of the Sped:rum, 

biit 



B O O K I. 7p 

but only to the Center of the Semicircle which 
bounded that end, or a little farther j and there- 
fore I compared this red not with that Colour 
which was exadlly in the middle of the Spedlrum, 
or Confine of green and blue, but with that which 
verged a little more to the blue than to the green : 
And, as I reckoned the whole Length of the 
Colours not to be the whole Length of the 
Spedjum, but the Length of its Redilinear Sides, 
fo compleating the femicircularEnds into Circles, 
when either of the obferved Colours fell within 
thofe Circles, I meafured the diftance of that 
Colour from the femicircular End of the Spe- 
drum, and fubdudting half this diftance from 
the meafured diftance of the two Colours, I 
took the Remainder for their corrected di- 
ftance; and in thefe Obfcrvations fet down this 
correfted diilance for the difference of the di- 
flances of their Foci from the Lens. For, as 
the Length of the Rectilinear Sides of the Spe- 
<3:rum would be the whole Length of all the 
Colours, were the Circles of which ( as we 
Ihewed) that Spedrum confifts contraded and 
reduced to Phyfical Points, fo in that Cafe this 
correded diftance would be the real diftance of 
the two obferved Colours. 

When therefore I farther obferved tlie deepcft 
fenfible red, and that blue whofe correded di- . 
ftance from it was i_ Parts of the Length of 
the Redilinear Sides of the Spedrum, the diffe- 
rence of the diftances of their Foci from the 
Lens was about 3^ Inches, and as 7 to 12, fo is 
3? ^o S'v 

When 



8o O P T I C K S. 

When I obferved the deepeft fenfible red, and 
that indigo whofe corredied diftance was ~ or | of 
the Length of the Rediilinear Sides of the Spe- 
(ftrum, the difference of the diftances of theii^ 
Foei from the Lens, was about 3I Inches, and as 
2 to 3, fois3|to 5I. 

When I obferved the deepefl fenfible red, and 
that deep indigo whofe corredted diftance from 
one another was ^ or l of the Length of the 
Rectilinear Sides of the Spectrum, the diffe- 
rence of the diftances of their Foci from the 
Lens was about 4 Inches -, and as 3 to 4, fo 
is 4 to 5|. 

When I obferved the deepeft feniible red, 
and that Part of the violet next the indigo, 
whofe corredled diftance from the red was {| 
or I of the Length of the Red:ilinear Sides of the 
Spedlrum, the difference of the diftances of their 
Foci from the Lens was about 4- Inches, and 
as 5 to 6, fo is 4i to 55. For fometimes, when 
the Lens was advantageoufly placed, fo that its 
Axis refpedted the blue, and all Things elfe 
were well ordered, and the Sun ftione clear, and 
1 held my Eye very near to the Paper on 
which the Lens caft the Species of the Lines, I 
could fee pretty diftind:ly the Species of thofe 
Lines by that Part of the violet which was next 
.the indigo J and fometimes I could fee them 
by above half the violet. For in making thefe 
Experiments I had obferved, that the Species 
of thofe Colours only appear diftindt, which were 
in or near the Axis of the Lens : So that if the 
blue or indigo were in the Axis, I could fee 
their Species diftindlyj and then the red ap- 
peared 



B O O K L 8i 

peared much kfs diftin6t than before. Wherefore 
I contrived to make theSped:riim of Colours flior- 
ter than before, fo that both its Ends might be 
nearer to the Axis of the Lens. And now its 
Length was about 2t Inches, and Breadth a^ 
bout r 01* i of ^^^ Inch. Alfo inftead of the 
black Lines on which the Spectrum was caft, I 
made one black Line broader than thofe, that I 
might fee its Species more eafily j and this Line I 
divided by Ihort crofs Lines into equal Parts, for 
meafuring the diflances of the obferved Colours. 
And now I could fometimes fee the Species of 
this Line with its Divifions almofl: as far as the 
Center of the femicircular violet End of the 
-Spedrunij and made thefe farther Obferva-^ 
tions. 

When I obferved the deepeft fenfible red, and 
that Part of the violet, whofe correfted diftance 
from it was about ' Parts of the Re<ftilinear Sides 
of the Spectrum, the Difference of the diftances 
of the Foci of thofe Colours from the Lens^ 
was one time 4], another time 47, another time 
4t Inches J and as 8 to 9, fo are 47, 4t> 4t, to 
5?> 5t'^^ 5^ refpedively. 

When I obferved the deepeft fenfible red,, 
and deepeft fenfible violet, ( the correded di- 
ftance of which Colours, when all Things were 
ordered to the beft Advantage, and the Sun 
(hone very clear, was about H or iy Parts of the 
Length of the Rectilinear Sides of the colour- 
ed Spedrum ) I found the Difference of the di- 
ftances of their Feci from the Lens fometimes 
4|- fometimes ^^y and for the moft part ^ In- 

G . ehgsi 



8i O P T I C K S. 

ches or thereabouts ; and as ii to 12, or 15 to 
16, fo is five Inches to 5* or 51. Inches. 

And by this ProgreiTion of Experiments I fatif- 
fied my felf, that had the Light at the very Ends 
of the Spedrum been ftrong enough to make the 
Species of the black Lines appear plainly on the 
Paper, the Focus of the deepefh violet would 
have been found nearer to the Lens, than the 
Focus of the deepeft red, by about 5^ Inches 
at leaft. And this is a farther Evidence, that 
the Sines of Incidence and Refradion of the fe- 
veral forts of Rays, hold the fame Proportion to 
one another in the fmallefl Refractions w^hich they 
do in the greateft. 

My Progrefs in making this^ice and trouble- 
fome Experiment I have fet down more at large, 
that they that iliall try it after me niay be aware 
of the Circumfpe(llion requifite to make it fuc- 
ceed well. And if they cannot make it fuc- 
ceed fo well as I did, they may notwithftand- 
ing coUedl by the Proportion of the diftance of 
the Colours of the Spedrum, to the Difference 
of the diftances of their Foci from the Lens, 
what would be the Succefs in the more diftant 
Colours by a better trial. And yet, if they ufe 
a broader Lens than I did, and fix it to a long 
ftrait Staif, by means of which it may be rea- 
dily and truly diredled to the Colour whofe Fo- 
cus is defired, I queftion not but the Experi- 
ment will fucceed better with them than it did 
with me. For I directed the Axis as nearly as I 
could to the middle of the Colours, and then 
the faint Ends of the Spedlrum being remote 
from the Axis, caft their Species lefs diflindtly 

1 on 



B O O K t 85 

on the Paper than they would have done, had the 
Axis been fucceffively diredled to them. 

Now by what has been faid, it's certain that the 
Rays which differ inRefrangibilitydo not converge 
to the fame Focus j but if they flow from a lucid 
Point, as far from the Lens on one fide as their 
Foci are on the other, the Focus of the moft re- 
frangible Rays fhall be nearer to the Lens than that 
of the leafl refrangible, by above the fourteenth 
Part of the whole diflance j and if they flow from 
a lucid Point, fo very remote from the Lens, that 
before their Incidence they may be accounted pa- 
rallel, the Focus of the moft refrangible Rays fliall 
be nearer to the Lens than the Focus of the kail 
refrangible, by about the 27th or 2 8 th Part of their 
whole diftance from it. And the Diameter of the 
Circle in the middle Space between thofe two 
Foci which they illuminate, when they fall there 
on any Plane, perpendicular to the Axis (which 
Circle is the leaft into which they can all be ga- 
thered ) is* about the 55th Part of the Diameter 
of the Aperture of the Glafs. So that 'tis a won- 
der, that Telefcopes reprefent Objeds fo diftindt 
as they do. But were all the Rays of Light 
equally refrangible, the Error ariflng only from 
the Sphericalnefs of the Figures of Glaffes would 
be many hundred times lefs. For, if the Obje6t- 
glafs of a Telefcope be Plano-convex, and the 
Plane fide be turned towards the Objedlj and 
the Diameter of the Sphere, whereof this Glafs 
is a Segment, be called D, and the Semidiame- 
ter of the Aperture of the Glafs be called S, and 
the Sine of Incidence out of Glafs into Air, be 
to the Sine of Refradtion as I to R j the Rays 

G 2 which 



84 O P T I C K S. 

w hich come parallel to the Axis of the Glafs, fhall 
in the Place where the Image of theObjed: is moft 
diflindly made, be fcattered all over a little Circle, 

whofe Diameter is — X very nearly, * as 

Iq Dquad. ^ ^' 

I gather by computing the Errors of the Rays by 
the Method of infinite Series, and rejecting the 
Terms, vi^hofe Quantities are inconfiderable. As 
for inflance, if the Sine of Incidence I, be to the 
Sine of Refradion R, as 20 to 3 1, and if D the 
Diameter of the Sphere, to which the Convex- 
fide of the Glafs is ground, be 100 Feet or 1200 
Inches, and S the Semidiametcr of the Aperture be 
two Inches, the Diameter of the little Circle, 

(that IS ^ -) will be , (or 

Iq ycD quad. 20 X 20 X 1 200 X i zoo 

961 X 

72000000 ) Parts of an Inch. But the Diameter of 

the little Circle, through which thefe Rays are 
fcattered by unequal Refrangibility, will be about 
the 55 th Part of the Aperture of the Objed-glafs, 
which here is four Inches. And therefore, the 
Error arifing from the Spherical Figure of the 
Glafs, is to the Error arifing from the different Re- 
frangibility of the Rays, as to - . that is 

*^ ■ •' ■' 72000000 rj* 

as I to 5449 ; and therefore, being in comparifon 
fo very little, deferves not to be confidered. 

But you will fay, if the Errors caufed by the 
different Refrangibility be fo very great, how 
comes it to pafs, that Objeds appear through 
Telefcopes fo diflind: as they do ? I anfwer, 'tis 

* Hovj to do this, is pezvn in our AuthorV Left. Optic. Part I. 
Se^. IV. Pnp.^x. 

becaufe 



B O O K I. 85 

becaufe the erring Rays are not fcattered uni- 
formly over all that Circular Space, but colleded 
infinitely more denfely in tlie Center than in 
any other Part of the Circle, and in the Way 
from the Center to the Circumference, grow 
continually rarer and rarer, fo as at the Circum- 
ference to become infinitely rare 5 and by rea- 
fon of their Rarity are not flrong enough to be 
vifible, unlefs in the Center and very near it. 
Let ADE [in Fig. 27.] reprefent one of thofe 
Circles defcribed with the Center C, and Semi- 
diameter AC, and let BFG be a finaller Circle 
concentrick to the former, cutting with its Cir- 
cumference the Diameter AC in B, and bife<fl 
AC in N } and by my reckoning, the Denfity of 
the Light in any Place B, will be to its Denfity 
in N, as AB to BC; and the whole Light with- 
in the Icffer Circle BFG, will be to the whole 
Light within the greater A ED, as the Excefs 
of the Square of A C above the Square of A B, 
is to the Square of AC. As if B C be the fifth 
Part of AC, the Light will be four times dcn- 
fer in B than in N, and the whole Light within 
the lefs Circle, will be to the whole Light with- 
in the greater, as nine to twenty-five. Whence 
it's evident, that the Light within the lefs Cir- 
cle, mufl ftrike the Senfe much more ftrongly, 
than that faint and dilated Light round about 
between it and the Circumference of the grea- 
ter. 

But it's farther to be noted, that the mcft lu- 
minous of the Prifmatick Colours are the yeU 
low and orange. Thefe aifed: the Senfes more 
ftrongly than all the reft together, and next to 

G 3 thefc 



S6 O P T I C K S. 

thefe in flrength are the red and green. Th^ 
blue compared with thefe is a faint and dark 
Colour, and the indigo and violet are fnuch 
darker and fainter, fo that thefe compared with 
the ftronger Colours are little to be regarded^ 
The Images of Ohjecfls are therefore to be pla-? 
ced, not in the Focus of the mean refrangible 
Rays, which are in the Confine of green and 
blue, but in the Focus of thofe Rays which are 
in the middle of the orange and yellow j therQ 
where the Colour is moil: luminous and fulgent^ 
that is in the brighteft yellow, that yellow which 
inclines more to orange than to green. And 
by the Refraction of thefe Rays (whofe Sines of- 
incidence and Refraction in Glafs are as 17 apd 
1 1 ) the Refradion of Glafs and Cryflal for Op- 
tical Ufes is to be meafured. Let us therefore 
place the Image of the Objed; in the Focus of 
thefe Rays, and all the yellow and orange will 
fall within a Circle, wnofe Diameter is about 
the 250th Part of the Diameter of the Aperture 
of the Glafs. And if you add the brighter half 
of the red, ( that half which is next the orange ) 
and the brighter half of the green, ( that half 
which is next the yellow ) about three fifth 
Parts of the Light of thefe two Coloi;irs will 
fall within the fame Circle, and two fifth Parts 
will fall without it round about y and that which 
falls without will be fpread through alinoil as 
much more fpace as that which falls within, 
and fo in the grofs be almoft three times rarer. 
Of the other half of the red and green, (that is 
of the deep dark red and willow green) about 
pne quarter will fall within this Circle, and 

three 



B O O K I. 87 

three quarters without, and that which falls 
without will be fpread through about four o^ 
five times more fpace than that which falls with- 
in ; and fo in the grofs be rarer, and if com 
pared with the whole Light within it, will be 
about 25 times rarer than all that taken in the 
grofs J or rather more than 30 or 40 times ra- 
rer, becaufe the deep red in the end of the 
Spedtmm of Colours made by a Prifm is very- 
thin and rare, and the willow green is fome- 
thing rarer than the orange and yellow. The 
Light of thefe Colours therefore being fo very 
much rarer than that within the Circle, will 
fcarce affe<5t the Senfe, efpecially fince the deep 
red and willow green of this Light, are much 
darker Colours than the reft. And for the fame 
reafon the blue and violet being much darker 
Colours than thefe, and much more rarified, 
may be neglected. For the denfe and bright 
Light of' the Circle, will obfcure the rare and 
weak Light of thefe dark Colours round about 
it, and render them almoft infenfible. The 
fenfible Image of a lucid Point is therefore 
fcarce broader than a Circle, whofe Diameter is 
the 250th Part of the Diameter of the Aperture 
of the Objedt-glafs of a good Telefcope, or not 
much brorder, if you except a faint and dark mifty 
Light round about it, which a Spectator wifr. 
fcarce regard. And therefore in a Telefcope, 
whofe Aperture is four Liches, and Length an 
hundred Feet, it exceeds not 2" 45'", or 3". And 
in a Telefcope whofe Aperture is two Inches, 
and Length 20 or 30 Feet, it may be 5" or 6", 
and fcarce above. And this anfwers well to 

G 4 Expe- 



88 O P T I C K S. 

Experience : For fpme Aftronomers have found 
the Diameters pf the fix'd Stars, in Telefcopes 
of between 20 and 60 Feet in length, to be a- 
bout 5" or 6", or at moft 8'' or 10" in diame- 
ter. But if the Eye-Glafs be tinfted faintly 
with the Smoak of a Lamp or Torch, to ob- 
fcure the Light of the Star, the fainter Light 
in the Circumference of the Star ceafes to be 
vilib .-, and the Star (if the Glafs be fufficiently 
foilta witli Smoak ) appears fomething more 
like a mathematical Point. And for the fame 
Reafon, the enormous Part of the Light in the 
Circumference of every lucid Point ought to be 
Icfs difcernible in fhorter Telefcopes than in lon- 
ger, becaufe the^fhorter tranfmit lefs Light to the 
Eye. 

Now, that the fix'd Stars, by reafon of their 
immenfe Diliance, appear like Points, unlefs fo 
far as tl^eir Light is dilated by Refra6lion, may 
appear from hence j that when the Moon pafTes 
over them and eclipfes them, their Light vanifhes, 
not gradually like that of the Planets, but all at 
once J and in the end of the Eclipfe it returns 
into Sight all at once, or certainly in lefs time 
than the fecond of a Minute ; the Refradion of 
the Moon's Atmofphere a little protrading th^ 
time in which the Light of the Star firfl vaniilies, 
^nd afterwards returns into Sight. 

NoWj if we fuppofe the fenfible Image of a lu- 
cid Point, to be even 250 times narrower than 
the Aperture of the Glafs 5 yet this Image would 
be fciil much greater than if it were only from 
th^ fpherical Figure of the' Glafs. For were 
i^ not for the different Refrangibility of the 

Raysj 



B O O K I. 8p 

Rays, its breadth in an loo Foot Tclefcope 

whofe aperture is 4 Inches, would be but ^- ^^^^ — 

parts of an Inch, as is manifeil by the foregoing 
Computation. And therefore in this cafe the 
greateft Errors arifing from the fpherical Figure 
of the Glafs, would be to the greateft fenfible 
Errors arihng from the different Refrangibihty 

of the Rays as ^^^^ to ^ at moft, that is on- 
ly as I to 1200. And this fufficiently (hews that 
it is not the fpherical Figures of Glalfes, but the 
different Refrangibihty of the Rays which hin- 
ders the perfeftion of Telefcopes. 

There is another Argument by w4iich it may 
appear that the different Refrangibihty of Rays, 
is the true caufe of the imperfed:ion of Tele- 
fcopes. For the Errors of the Rays arifmg from 
the fpherical Figures of Obje6t-glaffes, -Are as the 
Cubes of the Apertures of the Objed: Glaffes ; 
and thence to make Telefcopes of various 
Lengths magnify with equal diftindlnefs , the 
Apertures of the Objeft-glaffes, and the Charges 
or magnifying Powers ought to be as the 
Cubes of the fquare Roots of their lengths; 
which doth not anfwer to Experience. But 
the Errors of the Rays arifing from the different 
Refrangibihty, are as the Apertures of the Ob- 
jedt-glaffes ; and thence to make Telefcopes of 
various lengths, magnify with equal dillin6tnefs, 
their Apertures and Charges ought to be as the 
fquare Roots of their lengths ; and this anfwers 
to Experience, as is v/ell know^n. For Inffance, 
^ Tclefcope of 64 Feet in length, with an Aper- 

2 turQ 



90 O P T I C K S. 

ture of 2 1 Inches, magnifies about 120 times, 
with as much diftinftnefs as one of a Foot in 
length, with ^ of an Inch aperture, magnifies i^ 
times. 

Now were it not for this different Refrangi- 
bility of Rays, Telefcopes might be brought to 
a greater perfeftion than we have yet defcrib'd, 
by compofmg the Objedi-glafs of two Glaffes 
with Water between them. Let A D F C [in Fig, 
28.] reprefent the Objed:-glafs compofed of two 
Glaffes ABED and BEFC, alike convex on th® 
outfides AGD and CHF, and alike concave 
on the infides BME, BNE, with Water in 
the concavity BMEN. Let the Sine of Inci- 
dence out of Glafs into Air be as I to R, and 
out of Water into Air, as K to R, and by con- 
fequence out of Glafs into Water, as I to K: 
and let the Diameter of the Sphere to which the 
convex fides AGD and CHF are ground be 
D, and the Diameter of the Sphere to which 
the concave fides BME and BNE, are ground 
be to D, as the Cube Root of KK — KI to the 
Cube Root of R K-— R I : and the Refractions 
on the concave fides of the Glaffes, will very 
much corred the Errors of the Refradions on 
the convex fides, fo far as they arife from the 
fphericalnefs of the Figure. And by this means 
might Telefcopes be brought to fufiicient per- 
fection, were it hot for the different Refrangi- 
bility of feveral forts of Rays. But by reafon 
of this different Refrangibility, I do not yet fee 
any other means of improving Telefcopes by 
Refractions alone, than that of increafing their 
lengths, for which end the late Contrivance of 

Hugenhis 



B O O K I. pi 

Jlugenius feems well accommodated. For very 
long Tubes are cumberfome, and fcarce to be 
readily managed, and by reafon of their length 
are very apt to bend, and fhake by bending, fo 
as to cauie a continual trembling in the Objects, 
whereby it becomes difficult to fee them difl;in(fl- 
ly: whereas by his Contrivance the Glaffes are 
readily manageable, and the Objed-glafs being 
fix'd upon a flrong upright Pole becomes more 
fteady. 

Seeing therefore the Improvement of Tele- 
fcopes of given lengths by Refradions is defpe- 
ratej I contrived heretofore a Perfpedive by- 
Reflexion , ufmg inftead of an Objed-glafs a 
concave Metal. The diameter of the Sphere 
to which the Metal was ground concave was a- 
bout 25 Englijh Inches, and by confequence 
the length of the Inftrument about fix Inches 
and a quarter. The Eye-glafs v/as Plano-con- 
vex, and the diameter of the Sphere to which 
the convex iide was ground was about t of an 
Inch, or a little lefs, and by confequence it 
niagniiied between 30 and 40 times. By ano- 
ther way of meafuring I found that it magnified 
about 35 times. The concave Metal bore an 
Aperture of an Inch and a third part; but the 
Aperture was limited not by an opake Circle, 
covering the Limb of the Metal round about, 
but by an opake Circle placed between the Eye- 
glafs and the Eye, and perforated in the mid- 
dle with a little round hole for the Rays to pafs 
through to the Eye. For this Circle by being 
placed here, ftopp'd much of the errroneous 
Light, which otherwiie would have difturbed 

the 



p2 O P T I C K S. 

the Vifion. By comparing it with a pretty good 
Perfped;ive of four Feet in length, made with 
a concave Eye-glafs, I could read at a greater 
diftance with my own Inftrument than with the 
Glafs. Yet Objedts appeared much darker in 
it than in the Glafs, and that partly becaufe 
more Light was loft by Reflexion in the Metal, 
than by Refraction in the Glafs, and partly be- 
caufe my Inftrument was overcharged. Had it. 
magnified but 30 or 25 times, it would have 
made the Obje(5t appear more brisk and pleafant, 
Tv/o of thefe I made about 16 Years ago, and 
have one of them flill by me, by which I can 
prove the truth of v/hat I write. Yet it is not 
fo 2:ood as at the firft. For the concave has been 
divers times tarnifhed and cleared again, by rub- 
bing it with very foft Leather. When I made 
thefe an Artifl in London undertook to imitate it; 
but ufing another way of polifhing them than I 
did, he fell much fhort of what I had attained 
to, as I afterwards underftood by difcourfmg. 
the Under- work man he had employed. The 
Polifh I ufed was in this manner. I had 
two round Copper Plates, each fix Inches in 
Diameter, the one convex, the other concave,' 
ground very true to one another, On the con- 
vex I ground the Objedt-Metal or Concave 
which was to be polifli'd, 'till it had taken the 
Figure of the Convex and was ready for a 
Poliih. Then I pitched over the convex very' 
thinly, by dropping melted Pitch upon it, and 
warming it to keep the Pitch foft, whilft I 
ground it with the. concave Copper wetted 
to make it fpread eavenly all over the convex. 
^ Thus 



BOOK I. 95 

Thus by working it well I made it as thin as a 
Groat, and after the convex was cold I ground 
it again to give it as true a Figure as 1 could. 
Then I took Putty which I had made very fine 
by wafhing it from all its groiler Particles, and 
laying a little of this upon tlie Pitch, I ground 
it upon the Pitch with the concave Copper, till 
it had done making a Noife ; and then upon the 
Pitch I ground the Objed:-Metal with a brisk 
motion, for about two or three Minutes of 
time, leaning hard upon it. Then I put frefh. 
Putty upon the Pitch, and ground it again till it 
had done making a noife, and afterwards ground 
the Objed:-Metal upon it as before. And this 
Work I repeated till the Metal was poliflied, 
grinding it the laft time with all my llrength 
for a good while together , and frequently 
breathing upon the Pitch, to keep it moift with- 
out laying on any more frefli Putty. The Ob- 
jedl-Metal was two Inches broad, and about one 
third part of an Inch thick, to keep it from 
bending. I had two of thefe Metals, and when 
I had poliflied them both, I tried which was 
beft, and ground the other again, to fee if I could 
make it better than that which I kept. And 
thus by many Trials I learn'd the way of po- 
lifhing, till I made thofe two reflecting Perfpe- 
dlives I fpake of above. For this Art of po- 
lilhing will be better learn'd by repeated Pra- 
ctice than by my Defcription. Before I ground 
the Objedt-Metal on the Pitch, I always ground ' 
the Putty on it v/ith the concave Copper, till it 
had done making a noife, becaufe if the Parti- 
cles of the Putty were not by this means made 

to 



^4 O P T I C K S. 

to flick faft in the Pitch, they would by rolling 
up and down grate and fret the Objed-Metal and 
fill it full of little holes. 

But becaufc Metal is more difficult to polifll 
than Glafs, and is afterwards very apt to be 
fpoiled by tarnifhing, and reflects not fo much 
Light as Glafs quick-filver'd over does : I would 
propound to ufe inflead of the Metal, a Glafs 
ground concave on the forefide, and as much 
convex on the back-fide, and quick-filver'd o- 
ver on the convex fide. The Glafs mufl be e- 
very where of the fame thicknefs exactly. O- 
therwife it will make Objedls look colour'd and 
indiftind:. By fuch a Glafs I tried about five or 
fix Years ago to make a reflecfling Telefcope of 
four Feet in length to magnify about 150 times, 
and I fatislied my felf that there wants nothing 
but a good Artift to bring the Delign to perfe-- 
ftion. For the Glafs being wrought by one of 
our London Artifls after fuch a manner as they 
grind GlalTes for Telefcopes, though it feemed as 
well wrought as the Objed:-glaires ufe to be, yet 
when it was quick-filver'd, the Reflexion dif- 
covered innumerable Inequalities all over the 
Glafs. And by reafon of thefe Inequalities, Ob- 
jedls appeared indiftindl in this Inflrument. For 
the Errors of refledled Rays caufed by any Ine- 
quality of the Glafs, are about fix times greater 
than the Errors of refradled Rays caufed by 
the like Inequalities. Yet by this Experiment 
I fatisfied my felf that the Reflexion on the 
concave fide of the Glafs, which I feared would 
diflurb the Vifion, did no fenfible prejudice to 
it, and by confequence that nothing is wanting 

to 



B O O K I. p5 

to perfed thefe Telefcopes, but good Workmen 
who can grind and polifh GlaiTes truly fpherical. 
An Objedt-glafs of a fourteen Foot Telefcope, 
made by an Artificer at Lo?ido)i, I once mended 
confiderably, by grinding it on Pitch with Put- 
ty, and leaning very eafily on it in the grinding, 
left the Putty {hould fcratch it. Whether this 
way may not do well enough for polifhing thefe 
reflecting Glaffes, I have not yet tried. But he 
that Ihall try either this or any other way of po- 
liftiing which he may think better, may do well 
to make his GlafTes ready for poliihing, by grind- 
ing them without that Violence, wherewith our 
Londofi Workmen prefs their Glafles in grinding. 
For by fuch violent preiTure, Glafles are apt to 
bend a little in the grinding, and fuch bendino^ 
will certainly fpoil their Figure. To recom- 
mend therefore the confideration of thefe refled- 
ing GlaiTes to fuch Artifts as are curious in fi- 
guring GlafTes, I fliall defcribe this optical Inftru- 
ment in the following Propofition. 



PROP. VIII. Prob. II. 
To pjorten Telefcopes. 

LET ABDC [mFig.2g.] reprefent a Glafs 
fpherically concave on the forefide AB, and 
as much convex on the backfide CD, fo that 
it be every where of an equal thicknefs. Let it 
not be thicker on one fide than on the other, 
left it make Objects appear colour'd and indi- 

ftina, 



^6 O P T I C K S. 

flindl , and let it be very truly wrought and 
quick-filver'd over on the backfide; and fet in 
the Tube VXYZ which muft be very black 
within. Let EFG reprefent a Prifm of Glafs 
or Cryftal placed near the other end of the 
Tube, in the middle of it, by means of a han- 
dle of Brafs or Iron FGK, to the end of which 
made flat it is cemented. Let this Prifm be 
redangular at E, and let the other two Angles 
at F and G be accurately equal to each other, 
and by confequence equal to half right ones, 
and let the plane fides FE and GE be fquare, 
and by confequence the third fide F G a redlan- 
gular Parallelogram , whofe length is to its 
breadth in a fubduplicate proportion of two to 
one. Let it be fo placea in the Tube , that 
the Axis of the Speculum may pafs through the 
middle of the fquare fide EF perpendicularly 
and by confequence through the middle of the 
fide FG at an Angle of 45 Degrees, and let the 
fide E F be turned towards the Speculum, and 
the diftance of this Prifm from the Speculum 
be fuch that the Rays of the Light PQ, RS, ^c, 
which are incident upon the Speculum in Lines 
parallel to the Axis thereof, may enter the Prifm 
at the fide EF, and be reflected by the fide 
FG, and thence go out of it through the fide 
GE, to the point T, which muft be the com- 
mon Focus of the Speculum ABDC, and of a 
Plano-convex Eye-glafs H, through which thofe 
Rays muft pafs to the Eye. And let \ - Rays at 
their coming out of the. Glafs pafs . irough 
a fmall round hole, or aperture made in a lit* 
tie plate of Lead, Brafs, or Silver, wherewith 

the 



B O O K I. 97 

the Glafs is to be covered, which hole mufl be 
no bigger than is neceflary for Light enovigh to 
pafs through. For fo it will render the Objedt 
diftindt, the Plate in which 'tis made intercept- 
ing all the erroneous part of the Light which 
comes from the verges of the Speculum AB. 
Such an Inftrument well made, if it be fix Foot 
long, (reckoning the length from the Speculum 
to the Prifm, and thence to the Focus T ) will 
bear an aperture of fix Inches at the Speculum, 
and magnify between two and three hundred 
times. But the hole H here limits the aperture 
with more advantage, than if the aperture was 
placed at the Speculum. If the Inftrument be 
made longer or fhorter, the aperture muft be in 
proportion as the Cube of the fquare-fquare Root 
of the length, and the magnifying as the aper- 
ture. But it's convenient that the Speculum be 
an Inch or two broader than the aperture at the 
leaft, and that the Glafs of the Speculum be 
thick, that it bend not in the working. The 
Prifm EFG muft be no bigger than is necelTary, 
and its back lide FG muft not be quick-lilver'd 
over. For without quickfilver it will refledl all 
the Light incident on it from the Speculum. 

In this Inftrument the Objedl will be invertc^, 
but may be erected by making the fquare fides 
FF and EG of the Prifm EFG not plane but 
fpherically convex, that the Rays may crofs as 
well before they come at it as afterwards between 
it andj.rj-e Eye-glafs. If it be defired that the 
Inft^^ iie.it bear a larger aperture, that may be 
alfo Qone by compofmg the Speculum of two 
GlalTes with Water between them. 

H If 



pg O P T I C K S. 

If the Theory of making Telefcopes could at 
length be fully brought into Pradtice, , yet there 
would ' be certain Bounds beyond which Tele- 
fcopes could not perform. For the Air through 
which we look upon the Stars, is in a perpetual 
Tremor J as may be ften by the tremulous Moti- 
on of Shadows call: from high Towers,- and by- 
the twinkling of the fix'd Stars. But thefe Stars 
do not twinkle when viewed through Telefcopes 
which have large apertures. For the Rays of 
Light which pafs through divers parts of the 
aperture, tremble each of them apart, and by 
means of their various and fometimes contrary 
Tremors, fall at one and the fame time upon dif- 
ferent points in the bottom of the Eye, and their 
trembling Motions are too quick and confufed to 
be perceived feverally. And all thefe illuminated 
Points conftitute one broad lucid Point, com- 
pofed of thofe many trembling Points confufed- 
ly and infenlibly mixed with one another by very 
ihort and fwift Tremors, and thereby caufe the 
Star to appear broader than it is, and without 
any trembling of the whole. Long Telefcopes 
may caufe Objeds to appear brighter and larger 
than fliort ones can do, but they cannot be fo 
formed as to take away that confuiion of the 
Rays which arifes from the Tremors of the At- 
mofphere. The only Remedy is a moft ferene 
and quiet Air, fuch as may perhaps be found on 
the tops of the higheft Mountains above the grof- . 
ier Clouds. 



THE 




THE 

FIRST BOOK 



O F 



OPTICKS. 



PART II. 



PROP, I. Theor. I. 

T%e Phczno7nena of Colours hi refraEled or 
refie&ed Light are not caufed by new 
Modifications of the Light varioufly im- 
frefsd^ according to the various Termi- 
nations of the Light and Shadow. 



Exper. I. 



The Proof by Experiments. 



O R if the Sun fhine into a 
I very dark Chamber through 
an obiong hole F, [in Fig. i.] 
whofe breadth is tlie fixth or 
eighth part of an Inch, or fomething lefs j and 
his beam F H do afterwards pafs firft through a 

H 2 very 




i6o O P T i C K S. 

very large Prifm ABC, diftant about 20 Feet 
from the hole, and parallel to it, and then ( with 
it3 white part) through an oblong hole H, whofe 
breadth is about the fortieth or lixtieth part of 
an Inch, and which is made in a black opake 
Body GI, and placed at thediftanceof two or 
three Feet from the Prifm, 'in a parallel Situa- 
tion both to the Prifm and to the former hole, 
and if this white Light thus tranfmitted through 
the hole H, fall afterwards upon a white Paper 
//, placed after that hole H, at thediftanceof 
three or four Feet from it, and there paint thC; 
ufual ' Colours of the Prifm, fuppofe red at /, 
yellow at s, green at r, blue at ^, and violet 
at p ', you may with an Iron Wire, or any fuch 
like (lender opake Body, whofe breadth is a- 
bout the tenth part of an Inch, by intercepting 
the Rays at k, /, w, ;z or 0, take away any one 
of the Colours at t, s, r, q or />, whilft the other 
Colours remain upon the Paper as before j or 
with an Obftacle fomething bigger you may 
tak away any two, or three, or four Colours 
together, the reft remaining: So that any one 
of the Colours as well as violet may become 
outmoft in the Confine of the Shadow towards 
^, and any one of them as well as red may be- 
come outmoft in the Confine of the Shadow to- 
wards /, and any" one of them may alfo bor- 
der upon the Shadow made within the Colours 
by the Obftacle R intercepting fome interme- 
diate part of the Light; and, laftly, any one of 
them by being left alone, may border upon the 
Shadow on either hand. All the Colours have 
themfelves indifferently to any Confines of Sha- 

I dow. 



BOOK I. lor 

dow, and therefore the differences, of thefe Co- 
lours from one another, do not arife from the 
different Confines of Shadow, whereby Light 
is varioufly modified, as has hitherto been the 
Opinion of Philofophcrs. In trying thefe things 
*tis to be obferved, that by how much the holes 
F and H are narrower, and the Intervals be- 
tween them and the Prifm greater, and the 
Chamber darker, by fo much the better doth the 
Experiment fucceed ; provided the Light be 
not fo far diminifhed, but that the Colours at 
pt he fufficiently vifible. To procure a Prifm 
of folid Glafs large enough for this Experiment 
will be difficult, and therefore a prifmatick Vef- 
fel muft be made of poliili'd Glafs Plates ce- 
mented together, and filled with fait Water or 
clear Oil. 

Exper. 2. The Sun's Light let into a dark 
Chamber through the round hole F, [in Fig. 2.] 
half an Inch wide, paffed firft through the Prifm 
ABC placed at the hole, and then through a 
Lens PT fomething more than four Inches 
broad^ and about eight Feet diflant from the 
Prifm, and thence converged to O the Focus 
of the Lens diftant from it about three Feet, 
and there fell upon a white Paper D E. If that 
Paper was perpendicular to that Light incident 
upon it, as 'tis reprefented in the pollure DE, 
all the Colours upon it at O appeared white. 
But if the Paper being turned about an Axis 
parallel to the Prifm, became very much incli- 
ned to the Light, as 'tis reprefented in the Po- 
fitions de-Andi ^i-, the fame Light in the one 
cafe appeared yellow and red, in the other blue. 

H 3 Here 



102 O P T I C K S. 

Here one and the fame part of the Light in one 
and the fame place, according to the various In- 
clinations of the Paper, appeared in one cafe 
white, in another yellow or red, in a third blue, 
whilft the Confine of Light and Shadow, and 
the Refradions of the Prifm in all thefe cafes 
remained the fame. 

Expcr. 3. Such another Experiment may be 
more eaiily tried as follows. Let a broad beam 
of the Sun's Light coming into a dark Cham- 
ber through a hole in the Window-fhut be re- 
fracted by a large Prifm ABC, [in Fig. 3.] 
whofe refradting Angle C is more than 60 De- 
grees, and fo foon as it comes out of the Prifm, 
let it fall upon the white Paper DE glewed up- 
on a ilifF Plane; and this Light, when the Pa- 
per is perpendicular to it, as 'tis reprefented in 
DE, will appear perfed:ly white upon the Pa- 
per; but when the Paper is very much inclin'd 
to it in fuch a manner as to keep always paral- 
lel to the Axis of the Prifm, the whitenefs of 
the whole Light upon the Paper will according 
to the inclination of the Paper this way or that 
way, change either into yellow and red, as in 
the pofture J^, or into blue and violet, as in 
the pofture ^ e. And if the Light before it fall 
upon the Paper be twice refracted the fame 
way by two parallel Prifms, thefe Colours will 
become the more confpicuous. Here all the 
middle parts of the broad beam of white Light 
which fell upon the Paper, did without any 
Confine of Shadow to modify it, become co- 
lour'd all over with one uniform Colour, the 
Colour being always the fame in the middle of 

the 



B O O K I. 103 

the Paper as at the edges, and this Colour chan- 
ged according to the various Obliquity of the 
reflefting Paper, without any change in the Re- 
fradlions or Shadow, or in the Light which fell 
upon the Paper. And therefore thefe Colours 
are to be derived from fome other Caufe than the 
new Modifications of Light by Refradions and 
Shadows. 

If it be aiked, what then is their Caufe ? I 
anfwer, That the Paper in the poilure Jt', being 
more oblique to the more refrangible Rays than 
to the lefs refrangible ones, is more ilrongly illu- 
minated by the latter than by the former, and 
therefore the lefs refrangible Rays are predomi- 
nant in the refledted Light. And where-ever 
they are predominant in any Light, they tinge it 
with red or yellow, as may in fome meafure ap- 
pear by the firft Propofition of the firfl Part of 
this Book, and will more fully appear hereafter. 
And the contrary happens in the poflure cf the 
Paper ^e, the more refrangible Rays being then 
predominant which always tinge Light with 
blues and violets. 

Exper 4. The Colours of Bubbles with which 
Children play are various, and change their Si- 
tuation varioufly , without any refped to any 
Confine or Shadow. If fuch a Bubble be co- 
ver'd with a concave Glafs, to keep it from be- 
ing agitated by any Wind or Motion of the Air, 
the Colours will flowly and regularly change 
their Situation , even whilll the Eye and the 
Bubble, and all Bodies which emit any Light, 
or caft any Shadow , remain unmoved. And 
therefore their Colours arife from fome regular 

H 4 Caufe 



104 O P T I C K S. 

Caufe which depends not on any Confine of Sha- 
dow. What this Caufe is will be fliewed in the 
next Book. 

To thefe Experiments may be added the 
tenth Experiment of the firft Part of this firft 
Book, where the Sun's Light in a dark Room be- 
ing trajeded through the parallel Superficies of 
two Prifms tied together in the form of a Paralle- 
lopipede, became totally of one uniform yellow 
or red Colour, at its emerging out of the Prifms. 
Here, in the production of thefe Colours, the 
Confine of Shadow can have nothing to do. 
For the Light changes from white to yellow, 
orange and red fuccefiively, without any alte- 
ration of the Confine of Shadow : And at both 
edges of the emerging Light where the con- 
trary Confines of Shadow ought to produce 
different Effeds , the Colour is one and the 
fame, whether it be white, yellow, orange or 
red : And in the middle of the emerging Light, 
where there is no Confine of Shadow at all, the 
Colour is the very fame as at the edges, the 
whole Light at its very firft Emergence being of 
one uniform Colour, whether white, yellow, 
orange or red, and going on thence perpetual- 
ly without any change of Colour, fuch as the 
Confine of Shadow is vulgarly fuppofed to wotk 
in refradted Light after its Emergence. Nei- 
ther can thefe Colours arife from any new Mo- 
difications of the Light by Refradions, becaufe 
they change fuecefiively frorri white to yellow, 
orange and red, v^hile the Refradtions remain 
the fame, and alfo becaufe the Refradions are 
made contrary ways by parallel Superficies which 

deftro'y 



B O O K I. 105 

deftroy one another's Effeds. They arife not 
therefore from any Modifications of Light made 
byRefradions and Shadows, but have foire or her 
Caufe. What that Caufe is we (hewed abov-e in 
this tenth Experiment, and need not here re- 
peat it. 

There is yet another material Circumftance of 
this Experiment. For this emerging Light being 
by a third Prifm HIK" [in Fig. 22. Part L] re- 
fradled towards the Paper FT, and there painting 
theufual Colours of the Frifm, red, yellow, green, 
blue, violet : If thefe Colours arole from the Re- 
fradions of that Frifm modifying the Light, they 
would not be in the Light before its Incidence on 
that Frifm. And yet in that Experiment we 
found, that when by turning the two firft Prifms 
about their common Axis all the Colours were 
made to vanifh but the red; the Light which 
makes that red being left alone, appeared of 
the very fame red Colour before its Incidence 
on the third Frifm. And in general we find 
by other Experiments, that when the Rays 
which differ in Refrangibility are feparated from 
one another, and any one Sort of them is con- 
fidered apart, the Colour of the Light which 
they compofe cannot be changed by any Re- 
fraction or Reflexion whatever, as it ought to 
be were Colours nothing elfe than Modifica- 
tions of Light caufed by Refractions, and Re- 
flexions, and Shadows. This Unchangeablenefs 
of Colour I am now to defcribe in the following 
Propofition. 

PROP, 



io6 O P T I C K S. 

PROP. IT. Theor. II. 

u47/ homogeneal Light has its proper Colour 
anfweriftg to its Degree of Refrangibi- 
lity^ and that Colour cannot be changed 
by Reflexions and RefraSiions, 

IN the Experiments of the fourth Propofition 
of the firfh Part of this firft Book, when I had 
leparated the heterogeneous Rays from one ano- 
ther, the Spedrum pt formed by the feparated 
Rays, did in the Progrefs from its End^, on which 
the moft refrangible Rays fell, unto its other 
End /, on which the leaft refrangible Rays fell, 
appear tinged with this Series of Colours, violet, 
indigo, blue, green, yellow, orange, red, together 
with all their intermediate Degrees in a continual 
Succeffion perpetually varying. So that there ap- 
peared as many Degrees oi Colours, as there were 
forts of Rays differing in Refrangibility. 

Exper.^. Now, that thefe Colours could not be 
changed by Refradtion, I knew by refradiing with 
aPrifm fometimes one very little Part of tbisLight, 
fometimes another very little Part, as is defcribed 
in the twelfth Experiment of the firft Part of this 
Book. For by this Refradtion the Colour of the 
Light was never changed in the leaft. If any 
Part of the red Light was refracted, it remained 
totally of the fame red Colour as before. No 
orange, no yellow, no green or blue, no other 
new Colour was produced by that Refradtion. 
Neither did the Colour any ways change by 
repeated Refradtions, but continued always the 

fame 



B O O K I. 107 

fame red entirely as at firft. The like Con- 
ftancy and Immutability I found alfo in the blue, 
green, and other Colours. So alfo, if I looked 
through a Prifm upon any Body illuminated with 
any Part of this homogeneal Light, as in the four- 
teenth Experiment of the firfl Part of this Book 
is defcribed ; I could not perceive any new Co- 
lour generated this way. All Bodies illumina- 
ted with compound Light appear through Prifms 
confufed, (as was faid above) and tinged with 
various new Colours, but thofe illuminated with 
homogeneal Light appeared through Prifms 
neither lefs diflincfl, nor otherwife colour'd, 
than when viewed with the naked Eyes. Their 
Colours were not in the leaft changed by the 
Refrad:ion of the interpofed Prifm. I fpeak 
here of a fenfible Change of Colour : For the 
Light which I here call homogeneal, being not 
abfolutely homogeneal, there ought to arife 
fome little Change of Colour from its Hetero- 
geneity. But, if that Heterogeneity was fo lit- 
tle as it might be made by the faid Experiments 
of the fourth Propofition, that Change was not 
fenfible, and therefore in Experiments, where 
Senfe is Judge, ought to be accounted none 
at all. 

Exper. 6. And as thefe Colours were not 
changeable by Refradions, fo neither were they 
by Reflexions. For all white, grey, red, yel- 
low, green, blue, violet Bodies, as Paper, Afhes, 
red Lead, Orpiment, Lidico, Bife, Gold, Sil- 
ver, Copper, Grafs, blue Flowers, Violets, 
Bubbles of Water tinged with various Colours, 
Peacock's Feathers, the Tindure of Lignum 

NepbrU 






io8 G P T I C K S. 

Nephriticiwi^ and fuch-like, in red homogeneal 
Light appeared totally red, in blue Light totally 
blue, in green Light totally green, and fo of other 
Colours. In the homogeneal Light of any Cc- 
lour they all appeared totally of that fame Co- 
lour, with this only Difference, that fome of them 
reflected that Light more ftrongly, others more 
faintly. I never yet found any Body, which by 
reflecting homogeneal Light could fenfibly change 
its Colour. 

From all which it is manifeft, that if the Sun's 
Light confifted of but one fort of Rays, there 
wduld be but one Colour in the whole World, 
nor would it be poflible to produce any new Co- 
lour by Reflexions and Refradlions, and by confe- 
quence that the Variety of Colours depends upon 
the Compofition of Light. 

DEFINITION. 

TH E homogeneal Light and Rays which 
appear red, or rather make Obje<fls apr 
pear fo, I call Rubrifick or Red-making ; thofe 
which make Objects appear yellow, green, blue, 
and violet, I call Yellow-making, Green-making, 
Blue-making, Violet-making, and fo of the reft. 
And if at any time I fpeak of Light and Rays 
as coloured or endued with Colours, I would 
be underftood to fpeak not philofophically and 
properly, but grolly, and accordingly to fuch 
Conceptions as vulgar People in feeing all thefe 
Experiments would be apt to frame. For the 
Rays to fpeak properly are not coloured. In 
them there is nothing elfe than a certain Power 

and 



B O O K I. lop 

dndDifpofition to ftir up aSenfatlon of this or that 
Colour. For as Sound in a Bell or mufical String, 
or other founding Body, is nothing but a trem- 
bling Motion, and in the Air nothing but that 
Motion propagated from the Objed, and in the 
Senforium 'tis a Senfe of that Motion under the 
Form of Sound ; fo Colours in the Objedt are no- 
thing but a Difpofition to refledl this or that fort 
of Rays more copioufly than the reftj in the 
Rays they are nothing but their Difpolitions to 
propagate this or that Motion into the Senforium, 
and in the Senforium they are Senfations of thofe 
Motions under the Forms of Colours. 



PROP, III. Prob. I. 

To defifte the Refra77gibility of the fever al 
forts of homogeneal Light anfwering to 
the feveral Colours, 

FOR determining this Problem I made the 
following Experiment. * 
Exper, 7. When I had caufed the Redtilinear 
Sides AF, GM, [in /%4.] of the Spedrum of 
Colours made by the Prifm to be dirtiniflly de- 
fined,^ as in the fifth Experiment of the firft Part 
of this Book is defcribed, rhere were found in it 
all the homogeneal Colours in the fame Order 
and Situation one among another as in the 
Spe^rum of fimple Light, defcribed in the 
fourth Proportion of that Part. For the Cir- 
cles of which the Spedrum of compound Light 
* 5^^ «Ar AuthorV Lea. Optic. Partll. Se^.U. /. 239. 

PT 



jio O P T I C K S. 

P T is compofed, and which in the middle Parts 
of the Spectrum interfere, and are intermix'd with 
one another, are not intermix'd in their outmoft 
Parts where they touch thofe Redilinear Sides 
AF and GM. And therefore, in thofe Redi- 
linear Sides when diftindly defined, there is no 
n^w Colour generated by Refradlion. I obferved 
alfo, that if any where between the two outmoft 
Circles TMF and PGA a Right Line, as y^, 
w^as crofs to the Spectrum, fo as both Ends to 
fall perpendicularly upon its Rectilinear Sides, 
there appeared one and the fame Colour, and de- 
gree of Colour from one End of this Line to 
the other. I delineated therefore in a Paper 
the Perimeter of the Speft'rum FAP GMT, 
and in trying the third Experiment of the firft 
Part of this Book, I held the Paper fo that 
the Spe([lrum might fall upon this delineated 
Figure, and agree with it exactly, whilft an 
Affiiiant, whofe Eyes for diftinguilhing Colours 
were more critical than mine, did by Right 
Lines cc{Bj ^^, g^, &c. drawn crofs the Spe- 
ctrum, note the Confines of the Colours, that 
is of the red M a /3 F, of the orange a ^ ^ /3, 
of the yellow ye^^, of the green g ^9 ^, of the 
blue »iix9, of the indico iXfjua, and of the vio- 
let AGA^. And this Operation being divers 
times repeated both in the fame, and in feveral 
Papers, I found that the Obfervations agreed 
well enough with one another, and that the 
Redilinear Sides MG and FA were by the faid 
crofs Lines divided after the manner of a Mufi- 
cal Chord. Let GM be produced to X, that 
MX may be equal to GM, and conceive 
2 GX, 



BOOK L III 

GX, aX, iX, «X, gX, yX, aX, MX, to be 

in proportion to one another, as the Numbers, 
I, I, f, 1, f, f, i'tt, 4, and fo to reprefent the Chords 
of the Key, and of a Tone, a third Minor, a 
fourth, a fifth, a fixth Major, a feventh and an 
eighth above that Key : And the Intervals M a, 
ay, ye, in, »', 'A, and aG, will be tlie Spaces 
which the feveral Colours ( red, orange, yel- 
low, green, blue, indigo, violet ) take up. 

.Now thefe Intervals or Spaces fubtending the 
Differences of the Refradlions of the Rays go- 
ing to the Limits of thofe Colours, that is, to 
the Points M, a, y, g, y\, j, A, G, may without 
any fenfible Error be accounted proportional 
to the Difierences of the Sines of Refradion of 
thofe Rays having one common Sine of Inci- 
dence, and therefore fince the common Sine of 
Incidence of the mofl and leaft refrangible Rays 
out of Glafs into Air was ( by a Method defcri- 
bed above) found in proportion to their Sines 
of Refraction, as 50 to yy and 78, divide the 
Difference between the Sines of Refradiion 77 
and 78, as the Line GM is divided by thofe 
Intervals, and you will have 77, 77?, yy^, 77-f, 
77t> 77h 77iy 78, the Sines of Refradion of thofe 
Rays out of Glafs into Air, their common Sine 
of Incidence being 50. So then the Sines of 
the Incidences of all the red-making Rays out 
of Glafs into Air, were to the Sines of their Re- 
fradions, not greater than 50 to yy, nor lefs 
than 50 to yyiy but they varied from one ano- 
ther according to all intermediate Proportions. 
And the Sines of the Incidences of the green- 
making 



Ill O P T t C K S. 

making Rays were to the Sines of their Refradli-. 
ons in all Proportions from that of 50 to 'j'jl^ 
unto that of 50 to 'j'j^. And by the like Limits 
above-mentioned were the Refrddlions of the 
Rays belonging to the reft of the Colours .de- 
fined, the Sines of the red-making Rays extend- 
ing from 77 to 'j'j^^ thofe of the orange-making 
from 771- to.77-f, thofe of the yellow-making 
from j'j}^ to 77 j, thofe of the green-making 
from 'j'jy^ to "jji^^ thofe of the blue-making from 
77 i to 'J'j^i thofe of the indigo-making from 
'i']^ to ji^L^ and thofe of the violet from 77I to 

Thefe are the Laws of the Refradlons made 
out of Glafs into Air, and thence by the third 
Axiom of the iirfl Part of this Book, the Laws of 
the Refractions made out of Air into Glafs are ea- 
fily derived. 

Exper. 8. I found moreover, that when Light 
goes out of Air through feveral contiguous re- 
fracting Mediums as through Water and Glafs, 
and thence goes out again into Air, whether 
the refracting Superficies be parallel or inclin'd 
to one another, that Light as often as by con- 
trary Refractions 'tis fo corrected, that it emer- 
geth in Lines parallel to thofe in which it was 
incident, continues ever after to be white. But 
if the emergent Rays be inclined to the inci- 
dent, the Wnitenefs of the emerging Light will 
by degrees in paffing on from the Place of Emer- 
gence, become tinged in its Edges with Co- 
lours. This I try'd by refraCting Light with 
Prifms of Glafs placed within a Prifmatick Vef- 
iel of Water. Now thofe Colours argue a di- 
verging 



B O O K I. 113 

▼erging and feparation of the heterogeneous Rays 
from one another by means of their unequal Re- 
fractions, as in what follows will more fully ap- 
pear. And, on the contrary, the permanent 
whitenefs argues, that in like Incidences of the 
Rays there is no fuch feparation of the emerging 
Rays, and by confequence no inequality of their 
whole Refrad:ions. Whence I feem to gather 
the two following Theorems. 

1. The Exceffes of t-he Sines of Refracflion of 
feveral forts of Rays above their common SiAe of 
Incidence when the Refractions are made out of 
divers denfer Mediums immediately into one and 
the fame rarer Medium, fuppofe of Air, are to 
one another in a given Proportion. 

2. The Proportion of the Sine of Incidence 
to the Sine of Refradtion of one and the fame 
fort of Rays out of one Medium into another, 
is compofed of the Proportion of the Sine of 
Incidence to the Sine of Refradtion out of the 
firft Medium into any third Medium, and of the 
Proportion of the Sine of Incidence to the Sine 
of Refradtion out of that third Medium into the 
fecond Medium. 

By the firft Theorem the Refradtlons of the 
Rays of every fort made out of any Medium in- 
to Air are known by having the Refradtion of 
the Rays of any one fort. As for inftance, if 
the Refradtions of the Rays of every fort out 
of Rain-water into Air be defired, let the com- 
mon Sine of Incidence out of Glafs into Air be 
fubdudted from the Sines of Refradtion, and 

I the 



114 O P T I C K S. 

the ExcelTes will be 27, 27^, 27 1, 27J, ^jl, 
2j\, 275, 28. Suppofe now that the Sine of 
Incidence of the leaft refrangible Rays be to 
their Sine of Refraction out of Rain-water into 
Air as 3 to 4, and fay as i the difference of thofe 
Sines is to 3 the Sine of Incidence, fo is 27 the 
leaft of the ExcefTes above-mentioned to a fourth 
Number 8 1 j and 8 1 will be the common Sine of 
Incidence out of Rain-water into Air, to which 
Sine if you add all the abovementioned ExcefTes, 
you will have the defired Sines of the Refrad:ions 
108, io8f, 108-I, iq8', 108 ", 1085, io8|, 
109. 

By the latter Theorem the Refradlion out of 
one Medium into another is gathered as often 
£s you have the Refractions out of them both in- 
to any third Medium. As if the Sine of Inci- 
dence of any Ray out of Glafs into Air be to its 
Sine of Refradion, as 20 to 3 i, and the Sine of 
Incidence of the fame Ray out of Air into Wa- 
ter, be to its Sine of Refraction as 4 to 3; the 
Sine of Incidence of that Ray out of Glafs into 
Water will be to its Sine of RefraCtion as 20 to 3 1 
and 4 to 3 jointly, that is, as the FaCtum of '20 
and 4 to the FaCtum of 3 1 and 3, or as 80 to 93. 

And thefe Theorems being admitted into Op- 
ticks, there would be fcope enough of hand- 
ling that Science voluminoufly after a new man- 
ner *j not only by teaching thofe things which 
tend to the perfection of Vifion, but alfo-by 
determining mathematically all kinds of Phae- 
nomena of Colours which could be produced 

* Js is done in our Author'i Left. Optic. Part I. SeSl. III. and 
IV. and Par til. Se^. II. 

by 



BOOK I. rx5* 

by Refradlions. For to do this^ there is nothing 
elle requifite than to find out the Separations of 
heterogeneous Rays, and their various Mixtures 
and Proportions in every Mixture. By this way 
of arguing I invented almoft all the Phsenomena 
defcribed in thefe Books, befide fome others lefs 
neceffary to the Argument; and by the fuccelles 
I met with in the Trials, I dare promife, that to 
him who fhall argue truly, and then try all things 
with good 'Glaffes and fufficient Circumfpeclion, 
the cxpeded Event will not be wanting. But he 
is firft to know what Colours will arife from any 
others mix'd in any affigned Proportion. 

PROP. IV. Theor. hi. 
Colours may be produced by Compofttion 
ix^hich Jljall belike to the Colours of homO" 
■ geneal Light as to the Appear a7ice of Co- 
lour^ hut not as to the hrmiut ability of 
Colour and Co7iflitution of Light. Aftd 
thofe Colours by how much they are more 
co7npounded by fo much are they lefs full 
and inte?ife^ a?id by too much Compofition 
they may be diluted and weflke?id till they 
ceafey and the Mixture beco77ies white or 
grey, 'There may be alfo Colours produced 
by Compoftio?tj which are not fully like 
any of the Colours of homoge?2eal Light. 

FOR a Mixture of homogeneal red and yel- 
low compounds an Orauge, like in appea- 
I 2 ranee 



ii6 O P T I C K S. 

ranee of Colour to that orange which in the 
feries of unmixed prifmatick Colours lies between 
them; but the Light of one orange is homogeneal 
as to Refrangibility, and that of the other is he- 
terogeneal, and the Colour of the one, if viewed 
through a Prifm, remains unchanged, that of 
the other is changed and refolved into its compo- 
nent Colours red and yellow. And after the fame 
manner other neighbouring homogeneal Colours 
may compound new Colours , like the in- 
termediate homogeneal ones, as yellow and green, 
the Colour between them both, and afterwards, 
if blue be added, there will be made a green 
the middle Colour of the three which enter the 
Compofition. For the yellow and blue on either 
hand, if they are equal in quantity they draw the 
intermediate green equally towards themfelves in 
Compofition, and fo keep it as it were in i^qui- 
librio, that it verge not more to the yellow on the 
one hand, and to the blue on the other, but by 
their mix'd Actions remain ftill a middle Colour. 
To this mix'd green there may be farther added 
fome red and violet, and yet the green will not 
prefently ceafe, but only grow lefs full and vivid, 
and by increalingthe red and violet, it will grow 
more and more dilute, until by the prevalence of 
the added Colours it be overcome and turned into 
whitenefs, or fome other Colour. So if to the 
Colour of any homogeneal Light, the Sun's white 
Light compofed of all forts of Rays be added, 
tliat Colour will not vanifh or change its Species, 
but be diluted, and by adding more and more 
white it will be dikited more and more perpetu- 
ally. Laflly, If r^d and violet be mingled, there 
1 will 



B O O K I. 117 

will be generated according to their various Pro- 
portions various Purples, fuch as are not like in 
appearance to the Colour of any homogeneal 
Light, and of thefe Purples mix'd v^dth yellow 
and blue may be made other nev^ Colours. 



PROP. V. Theor. IV. 
Whiumjs and all grey Colours hetwee?i 
white and blacky may be compounded of 
Colours^ and the whitenefs of the Suns 
Light is compounded of all the primary 
^Colours mix'd in a due Proportion, 

The Proof by Experiments. 
Exper. 9.np H E Sun fliining into a dark Cham- 

-*- ber through a little round hole in 
the Window-fliut , and his Light being there 
refraded by a Prifm to cafl his coloured Image 
PT [in Fig. 5.] upon the oppofite Wall : I held 
a white Paper V to that Image in fuch manner 
that it might be illuminated by the colon r'd 
Light refle(5ted from thence, and yet not inter- 
cept any part of that Light in its paflage from 
the Prifm to the Spectrum. And I found that 
when the Paper was held nearer to any Colour 
than to the reft, it appeared of that Coiour to 
which it approached neareft^ but when it was 
equally or almoft equally diftant from all the 
Colours, fo that it might be equally illumina- 
ted by them all it appeared white. And in this 
laft fituation of the Paper, if fome Colours were 

I 3 inter- 



ii8 O P T I C K S. 

, intercepted, the Paper loft its white Colour, and 
appeared of the Colour of the reft of the Light 
which was not intercepted. So then the Pa- 
per was illuminated with Lights of various Co- 
lours, namely, red, yellow, green, blue and 
violet, and every part of the Light retained its 
'proper Colour, until it was incident on the Pa- 
per, and became refleded thence to the Eycj 
fo that If it had been- either alone ( the reft of 
the Light being intercepted ) or if it had a- 
bounded moft , and been predominant in the 
Light refled:ed from the Paper, it would have 
tinged the Paper with its own Colour j and yet 
being mixed with the reft of the Colours in a 
due pi:oporti6n, it made the Paper look white, 
and therefore by a Compoiition with the reft 
produced that Colour. The feveral parts of 
the coloured Light refleded from the Spectrum, 
whilft they are propagated from thence through 
the Air, do perpetually retain their proper Co- 
lours, becaufe wherever they fall upon the Eyes 
of any Spedator, they m.ake the feveral parts of 
the Spectrum to appear under their proper Co- 
lours. They retain therefore their proper Co- 
lours when they fall. upon the Paper V, and fo 
\)y the confuficn and perfed: mixture of thofe' 
Colours compound the whitenefs of the Light 
refleded from thence. 

Expcr. lo. Let that Spe6trum or folar Image 
]^T [in Fig. 6,'\ f^ll now upon the Lens MN 
above four Liches broad, and about fix Feet di- 
ftarit fi'om the Prifm ABC and fo figured that 
it may caufe the coloured Light which diverg-^ 
^ph from the Prifm to converge and meet again- 

"i a*. 



"B O O K I. iig 

at its Focus G, about fix or eight Feet diflant 
from the Lens, and there to fall perpendicularly 
upon a white Paper DE. And if you move 
this Paper to and fro, you will perceive that 
near the Lens, as at de^ the whole folar Image 
(fuppofe 2X pt) will appear upon it intenfely 
coloured after the manner above-explained, and 
that by receding from the Lens thofe Colours 
will perpetually come towards one another, and 
by mixing more and more dilute one another 
continually, until at length the Paper come to 
the Focus G, where by a perfed: mixture they 
will wholly vanifh and be converted into white- 
nefs, the whole Light appearing now upon the 
Paper like a little white Circle. And after- 
wards by receding farther from the Lens, the 
Rays which before converged will now crofs 
one another in the Focus G, and diverge from 
thence, and thereby make the Colours to appear 
again, but yet in a contrary order; fuppofe at 
^i, where the red t is now above which before 
was below, and the violet p is below which be- 
fore was above. 

Let us now flop the Paper at the Focus G, 
where the Light appears totally white and cir- 
cular, and let us confider its whitenefs. I fay, 
that this is compofed of the converging Colours. 
For if any of thofe Colours be intercepted at 
the Lens, the whitenefs will ceafe and degene- 
rate into that Colour which arifeth from the 
compofition of the other Colours which are not 
intercepted. And then if the intercepted Co- 
lours be let pafs and fall upon that compound 
Colour, they mix with it, and by their mixture 

I 4. reilore 



I20 O P T I C K S. 

ilore the whitenefs. So if the violet, blue and 
green be intercepted, the remaining yellow, 
orange and red will compound upon the Paper 
an orange, and then if the intercepted Colours 
be let pafs, they will fall upon this compounded 
orange, and together with it decompound a 
white. So alfo if the red and violet be inter- 
cepted, the remaining yellow, green and blue, 
will compound a green upon the Paper, and 
then the red and violet being let pafs will fall up- 
on this green, and together with it decompound 
a white. And that in this Compoiition of white 
the feveral Rays do not fuffer any Change in their 
colorific Qualities by ading upon one another, 
but are only mixed, and by a mixture of their 
Colours produce white, may farther appear by 
thefe Arguments. 

If the Paper be placed beyond the Focus G, 
fuppofe at h^i, and then the red Colour at the 
Lens be alternately intercepted, and let pafs a- 
gain, the violet Colour on the Paper will not fuf^ 
fer any Change thereby, as it ought to do if the 
feverai forts of Rays adted upon one another in 
the Focus G, where they crofs. Neither will 
the red upon the Paper be changed by any alter- 
nate flopping, and letting pafs the violet which 
crolieih it. 

And if the Paper be placed at the Focus G, 
and the white round Image at G be viewed 
through the Pnfm HIK, and by the Refradiion 
of that Prifm be tranllated to the place ri', and 
there sppear tinged with various Colours, name- 
ly, the violet at v and red at r, and others be- 
tween, and then the red Colours at the Lens 

be 



B O O K I. 121 

be often ftopp'd and let pafs by turns, the red 
at r will accordingly difappear, and return as of- 
ten, but the violet at v will not thereby fuffer any 
Change. And fo by flopping and letting pafs 
alternately the blue at the Lens, the blue at v 
will accordingly difappear and return, without 
any Change made in the red at r. The red there- 
fore depends on one fort ot Rays, and the blue 
on another fort, which in the Focus G v/here 
they are commix'd, do not acTt on one another. 
And there is the fame Reafon of the other Co- 
lours.* 

I confidered farther, that when the moft re- 
frangible Rays P/>, and the leaft refrangible 
ones T t, are by converging inclined to one ano- 
ther, the Paper, if held very oblique to thofe 
Rays in the Focus G, might refled: one fort of 
them more copioully than the other fort, and 
by that Means the remedied Light would be 
tinged in that Focus with the Colour of the pre- 
dominant Rays, provided thofe Rays feverally 
retained their Colours, or coloriiic Qualities in 
the Compofition of White made by them, in tliat 
Focus. But if they did not retain them in that 
White, but became all of them feverally endued 
there with a Difpof^tion to flrike the Senfe with 
the Perception of White, then they could never 
lofe their Whitenefs by fuch Reflexions. I in- 
clined therefore the Paper to the Rays very oblique- 
ly, as in the fecond Experiment of this fecondPart 
of the firft Book, that the moft refrangible Rays 
might be more copioufiy refieded than the refl, 
and the Whitenefs at Length changed fucceffively 
into blue, indigo, and violet. Then I inclined it 

the 



122 O P T I C K S. 

the contrary Way, that the leaft refrangible Rays 
might be more copious in the reflected Light than 
the reft, and the Whitenefs turned fucceffively to 
yellow, orange, and red. 

Laftly, I made an Inftrument X Y in fafhion 
of a Comb, whofe Teeth being in number fix- 
teen, were about an Inch and an half broad, and 
the Intervals of the Teeth about two Inches 
wide. Then by interpofmg fucceffively the 
Teeth of this Inftrument near the Lens, I inter- 
cepted Part of the Colours by the interpofed 
Tooth, whilft the reft of them went on through 
the Interval of the Teeth to the Paper DE, and 
there painted a round Solar Image. But the Pa- 
per I had iirft placed fo, that the Image might 
appear white as often as the Comb was taken 
away j and then the Comb being as was faid in- 
terpofed, that Whitenefs by reafon of the inter- 
cepted Part of the Colours at the Lens did al- 
ways change into the Colour compounded of 
thofe Colours which were not intercepted, and 
that Colour was by the Motion of the Comb 
perpetually varied fo, that in the paffing of every 
Tooth over the Lens all thefe Colours, red, yel- 
low, green, blue, and purple, did alw^ays fuc- 
ceed one another. I caufed therefore all the 
Teeth to pafs fucceffively over the Lens, and 
when the Motion w^as flow, there appeared a 
perpetual Succeffion of the Colours upon the 
Paper : But if I fo much accelerated the Mo- 
tion, that the Colours by reafon of their quick 
Succeffion could not be diftinguiffied from one 
another, the Appearance of the fmgle Colours 
ceafed. There was no redj no yellow, nq 

green. 



B O O K I. 123 

green, no blue, nor purple to be feen any lon- 
ger, but from a Confulion of rhem all there a- 
rofe one uniform white Colour. Of the Light 
which now by the Mixture of all the Colours ap- 
peared white, there was no Part really white. 
One Part was red, another yellow, a third green, 
a fourth blue, a fifth purple, and every Part re-» 
tains its proper Colour till it ftrike the Senfo- 
rium. If the Impreffions follow one another 
flowly, fo that they may be feverally perceived, 
there is made a diftind: Senfation of all the Co- 
lours one after another in a continual SucceA 
fion. But if the Impreffions follow one ano- 
ther fo quickly, that they cannot be feverally 
perceived, there arifeth out of them all one 
common Senfation, which is neither of this 
Colour alone nor of that alone, but hath it felf 
indifferently to 'em all, and this is a Senfation 
of Whitenefs. By the Quicknefs of the Succei^ 
lions, the Impreffions of the feveral Colours are 
confounded in the Senforium, and out of that 
Confufion arifeth a mix'd Senfation. If a burn- 
ing Coal be nimbly moved round in a Circle 
with Gyrations continually repeated, the whole 
Circle will appear like Fire ; the reafon of which 
is, that the Senfation of the Coal in the feve- 
ral Places of that Circle remains imprefs'd on 
the Senforium, until the Coal return again to 
the fame Place. And fo in a quick Confecu- 
tion of the Colours the Impreffion of every Co- 
lour remains in the Senforium, until a Revolu- 
tion of all the Colours be compleated, and that 
firit Colour return again. The Impreffions there- 
fore of all the fucceffive Colours are at once in 

the 



124 O P T I C K S. 

the Senforium, and jointly ftir up a Senfation of , 
them all ; and fo it is manifeft by this Experi- 
inent, that the commix'd Impreffions of all the 
Colours do ilir up and beget a Senfation of white, 
that is, that Whitenefs is compounded of all the 
Colours. 

And if the Comb be now taken away, that all 
the Colours may at once pafs from the Lens to 
the Paper, and be there intermixed, and toge- 
ther refleded thence to the Spectator's Eyes; their 
Impreffions on the Senforium being now more 
fubtilly and perfe(5lly commixed there, ought 
much more to ftir up a Senfation of White- 
nefs. 

You may inftead of the Lens ufe two Prifms 
HIK and LMN, which by refracting the co- 
loured Light the contrary Way to that of the 
^rft Refraction, may make the diverging Rays 
converge and meet again in G, as you fee repre-, 
fented in the feventh Figure. For where they 
meet and mix, they will Qompofe a white Light, 
as when a Lens is ufed. 

Exper. 1 1. Let the Sun's coloured Image P T 
[in Fig. 8.] fall upon the Wall of a dark Cham- 
ber, as in the third Experiment of the firft Book, 
and let the fame be viewed through a Prifm 
aifCy held parallel to the Prifm ABC, by whofe 
Refraction that Image was made, and let it now 
appear lower than before, fuppofe in the Place 
S over-againft the red Colour T. And if you 
go near to the Liiage P T, the SpeCtrum S will 
appear oblong and coloured like the Image P T $ 
but if you recede from it, the Colours of the 
SpeCtrum S will be contracted more and more, 

and 



B O O K T. 125 

and at length vanifli, that Sped:rum S becoming 
perfedly round and white j and if you recede yet 
farther, the Colours will emerge again, but in a 
contrary Order. Now that Spedlrum S appears 
white in that Cafe, when the Rays of feveral 
forts which converge from the feveral' Parts of 
the Image P T, to the Prifm abc, are fo re- 
fradted unequally by it, that in their PalTage 
from the Prifm to the Eye they may diverge 
from one and the fame Point of the Spedirum 
S, and fo fall afterwards upon one and the 
fame Point in the bottom of the Eye, and there 
be mingled. 

And farther, if the Comb be here made ufe of, 
by whofe Teeth the Colours at the Image PT 
may be fucceffively intercepted ; the Spe(ftrum S, 
when the Comb is moved llowly, will be perpe- 
tually tinged with fucceiTive Colours: But when 
by accelerating the Motion of the Comb, the 
Succeffion of the Colours . is fo quick that they 
cannot be feverally feen, that Spedrum S, by a 
confufed and mix'd Senfation of them all, will 
appear white. 

Exper. 12. The Su.i ihining* through a large 
Prifm ABC [in Fig, 9.] upon a Comb X Y, 
placed immediately behind the Prifm, his Light 
which pafTed through the Interftices of the 
Teeth fell upon a white Paper D E. The 
Breadths of the Teeth were equal to their In- 
terftices, and feven Teeth together w^th their 
Interftices took up an Inch in Breadth. Now, 
when the Paper was about two or three Inches 
diftant from the Comb, the Light which paf- 
fed through its. feveral Interftices painted fo 

many 



126 O P T I C K S. 

many Ranges of Colours, kl^ mn, op^ qr^ &c. 
which were parallel to one another^ and conti- 
guous, and without any Mixture of white. And 
thefe Ranges of Colours, if the Comb was moved 
continually up and down with a reciprocal Mo- 
tion, afcended and defcended in the Paper, and 
when the Motion of the Comb was fo quick, that 
the Colours could not be diftinguiflied from 
one another, the whole Paper by their Con- 
fufion and Mixture in the Senforium appeared 
white. 

Let the Comb now reft, and let the Paper 
be removed farther from the Prifm, and the fe- 
veral Ranges of Colours will be dilated and 
expanded into one another more and more, and 
by mixing their Colours will dilute one ano- 
ther, and at length, when the diftance of the 
Paper from the Comb is about a Foot, or a 
little more (fuppofe in the Place 2D 2E) they 
will fo far dilute one another, as to become 
white. 

With any Obftacle, let all the Light be now 
ftopp'd which paffes through any one Literval 
of the Teeth, fo that the Range of Colours which 
comes from thence may be taken away, and 
you will fee the Light of the reft of the Ranges 
to be expanded into the Place of the Range taken 
away, and there to be coloured. Let the in- 
tercepted Range pafs on as before, and its Co- 
lours falling upon the Colours of the other 
Ranges, and mixing with them, will reftore the 
Whitenefs. 

Let the Paper 2 D 2 E be now very much in- 
clined to the RaySj fo that the moft refrangible 

Rays 



BOOK I. 127 

Rays may be more copioufly refleded than the 
reft, and the white Colour of the Paper through 
the Excefs of thofe Rays will be changed into 
blue and violet. Let the Paper be as much in- 
clined the contrary way, that the leaft refran- 
gible Rays may be now more copioufly refledl- 
ed than the reft, and by their Excefs the White- 
nefs will be changed into yellow and. red. The 
feveral Rays therefore in that white Light do 
retain their colorific Qualities, by which thofe 
of any fort, whenever they become more co- 
pious than the reft, do by their Excefs and Pre- 
dominance caufe their proper Colour to ap- 

And by the fame way of arguing, applied to the 
third Experiment of this fecond Part of the firft 
Book, it may be concluded, that the white Colour 
of all refracted Light at its very firft Emergence, 
where it appears as white as before its Incidence, 
is compounded of various Colours. 

Exper, 13. In the foregoing Experiment the 
feveral Intervals of the Teeth of the Comb do 
the Office of fo many Prifms, every Interval pro- 
ducitig the Phcenomenon of one Prifm. Whence 
inftead of thofe Intervals ufing feveral Prifms, 
I try'd to compound Whitenefs by mixing their 
Colours, and did it by ufing only three Prifms, 
as alfo by ufing only two as follows. Let two 
Prifms ABC and a be, [in Fig. 10.] whofe re- 
frading Angles B and b are equal, be fo placed 
parallel to one another, that the refrading An- 
gle B of the one may touch the Angle c at the 
Bafe of the other, and their Planes C B and 
cbj at which the Rays emerge, may lie in Di- 

redum. 



128 O P T I C K S. 

re(5luin. Then let the Light trajedied through 
them fall upon the Paper M N, diiftant about 8 
or 12 Inches from the Prifms. And the Co- 
lours generated by the interior Limits B and c 
of the two Prifms, will be mingled at P T, and 
there compound white. For if either Prifm be 
taken away, the Colours made by the other will 
appear in that Place P T, and when the Prifmi 
is reftored to its Place again, fo that its Co- 
lours may there fall upon the Colours of the 
other, the Mixture of them both will reftore the 
White nefs. 

This Experiment fucceeds alfo, as I have tried, 
when the Angle b of the lower Prifm, is a lit- 
tle greater than the Angle B of the upper, and 
between the interior Angles B and f, there in- 
tercedes fome Space B c, as is reprefented in 
the Figure, and the refrading Planes B C and 
b c, are neither in Directum, nor parallel to one 
another. For there is nothing more requilite 
to the Succefs of this Experiment, than that 
the Rays of all forts may be uniformly mixed 
upon the Paper in the Place P T. If the moft 
refrangible Rays coming from the fuperior 
Prifm take up all the Space from M to P, the 
Rays of the fame fort which come from the in- 
ferior Prifm ought to begin at P, and take up 
all the reft of the Space from thence towards 
N. If the leaft refrangible Rays coming from 
the fuperior Prifm take up the Space M T, the 
Rays of the fame kind which come from the 
other Prifm ought to begin at T, and take up 
the remaining Space TIN. If oric fort of the 
Rays which have intermediate Degrees of Re- 

frangibility, 



B O O K I. 129 

frangibillty, and come from the fuperlor Prifm 
be extended through the Space M Q^ and ano- 
ther fort of thofe Rays through the Space M JR., 
and a third fort of them through the Space M S, 
the fame forts of Rays coming from the lower 
Prifm, ought to illuminate the remaining Spaces 
QN, R N, S N, refpedively. And the fame is 
to be underftood of all the other forts of Rays. 
For thus the Rays of every fort will be fcattered 
uniformly and evenly through the whole Space 
MN, and fo being every where mix'd in the fame 
Proportion, they muft every where produce the 
fame Colour. And therefore, fince by this Mix- 
ture they produce white in the Exterior Spaces 
MP and TN, they muft alfo produce white 
in the Interior Space PT. This is the reafon 
of the Compolition by which Whitenefs was pro- 
duced in this Experiment, and by what other 
way foever I made the like Compofition, the Re- 
fult was Whitenefs. 

Laftly, If with the Teeth of a Comb of a due 
Size, the coloured Lights of the two Prifms 
which fall upon the Space PT be alternately in- 
tercepted, that Space P T, when the Motion of 
the Comb is flow, will always appear coloured, 
but by accelerating the Motion of the Comb fo 
much that the fucceffive Colours cannot be 
diftinguifhed from one another, it will appear 
white. 

Exper, 14. Hitherto I have produced White- 
nefs by mixing the Colours of Prifms. If now 
the Colours of natural Bodies are to be min- 
gled, let Water a little thicken'd with Soap be 
agitated to raife a Froth, and after that Froth 

K has 



130 O P T I C K S. 

has ftood a little, there will appear to one that 
{hall view it intently various Colours every where 
in the Surfaces of the feveral Bubbles j but to 
one that fliall go fo far off, that he cannot diftin- 
guifh the Colours from one another, the whole 
Froth will grow white with a perfedl White- 
nefs. 

Exper. 15. Laftly, In attempting to compound 
a white, by mixing the coloured Powders which 
Painters ufe, I conlider'd that all coloured Pow- 
ders do fupprefs and flop in them a very confi- 
derable Part of the Light by which they are illu- 
minated. For they become coloured by refledl- 
ing the Light of their own Colours more co- 
pioufly, and that of all other Colours more fpa- 
ringly, and yet they do not refied: the Light of 
their own Colours fo copioufly as white Bodies 
do. If red Lead, for inflance, and a white Pa- 
per, be placed in the red Light of the colour'd 
Spedtrum made in a dark Chamber by the Re- 
fraction of a Prifm, as is defcribed in the third 
Experiment of the firfl Part of this Book ; the Pa- 
per will appear more lucid than the red Lead, 
and therefore refledis the red-making Rays more 
copioufly than red Lead doth. And if they be 
held in the Light of any other Colour, the 
Light reiledled by the Paper will exceed the 
Light reflefted by the red Lead in a much 
greater Proportion. And the like happens in 
Powders of other Colours. And therefore by 
mixing fuch Powders, we are not to exped; a 
flrong and full White, fuch as is that of Pa- 
per, but fome dusky obfcure one, fuch as might 
arife from a Mixture of Light and Darknefs, 

I or 



BOOK I. 131 

or from white and black, that is, a grey, pr 
dun, or ruflet brown, fuch as are the Colours' 
of a Man's Nail, of a Moufe, of Afhcs, of or- 
dinary Stohes, of Mortar, of Dull: and Dirt in 
High-ways, and the like. And fuch a dark white 
I have often produced by mixing colour 'd Pow- 
ders. For thus one Part of red Lead, and five 
Parts of Viridc lEris, compofed a dun Colour 
like that of a Moufe. For thefe two Colours 
were feverally fo compounded of others, that 
in both together were a Mixture of all Co- 
lours; and there was lefs red Lead ufed than 
Viride Mr is, becaufe of the Fulnefs of its Co- 
lour. Again, one Part of red Lead, and four 
Parts of blue Bife, compofed a dun Colour 
verging a little to purple, and by adding to 
this a certain Mixture of Orpiment and Viride 
Mris in a due Proportion, the Mixture loft its 
purple TinQure, and became perfed:ly dun. 
But the Experiment fucceedcd belt without Mi- 
nium thus. To Orpiment I added by little 
and little a certain full bright purple, which 
Painters ufe, until the Orpiment ceafed to be 
yellow, and became of a pale red. Then I di- 
luted that red by adding a little Vitide JEris, 
and a little more blue Bife than Viride Mris, un- 
til it became of fuch a "grey or pale white, as 
verged to no one of the Colours more than to 
another. For thus it became of a Colour equal 
in Whitenefs to that of Afhes, or of Wood newly 
cut, or of a Man's Skin. The Orpiment re- 
fledled more Light, than did any other of the 
Powders, and therefore conduced more to the 
Whitenefs of the com.pounded Colour than thev. 
. K 2 fo 



132 O P T I C K S. 

To affign the Proportions accurately may be diffi- 
cult, by reafon of the different Goodnefs of Pow- 
ders of the fame kind. Accordingly, as the Co- 
lour of any Powder is more or lefs full and lumi- 
nous, it ought to be ufed in a lefs or greater Pro- 
portion. 

Now, confidering that thefe grey and dun Co- 
lours may be alfo produced by mixing Whites 
and Blacks, and by confequence differ from 
perfedt Whites, not in Species of Colours, but 
only in degree of Luminoufnefs, it is manifefl that 
there is nothing more requifite to make them 
perfectly white than to increafe their Light fuffici- 
ently ; and, on the contrary, if by increafmg 
their Light they can be brought to perfedl White- 
nefs, it will thence alfo follow, that they are of 
the fame Species of Colour with the beft Whites, 
and differ from them only in the Quantity of 
Light. And this I tried as follows. I took the 
third of the above-mention'd grey Mixtures, ( that 
which was compounded of Orpiment, Purple, 
Biie. and Viride Mrh ) and rubbed it thickly 
upon the Floor of my Chamber, where the Sun 
{hone upon it through the opened Cafement ; 
and by it, in the fhadow, I laid a Piece of white 
Paper of the fame Bignefs. Then going from 
them to the diflance of 12 or 18 Feet, fo that 
I could not difcern the Unevennefs of the Sur- 
face of the Powder, nor the little Shadows let 
fall from the gritty Particles thereof j the Pow- 
der appeared intenfely white, fo as to tranfcend 
even the Paper it felf in Whitenefs, efpecially 
if the Paper were a little fliaded from the Light 
of the Clouds, and then the Paper compared 
5 with 



,A 



B O O K I. 133 

with the Powder appeared of fuch a grey Colour 
as the Powder had done before. But by laying 
the Paper where the Sun fliines through the 
Glafs of the Window, or by fhutting the Win- 
dow that the Sun might fhine through the Glafs 
upon the Powder, and by fuch other fit Means of 
iiicreafing or decreafnig the Lights wherewith the 
Powder and Paper were illuminated, the Light 
wherewith the Powder is illuminated may be* 
made ilronger in fuch a due Proportion than 
the Light wherewith the Paper is illuminated, 
that they fhall both appear exadly alike in 
Whitenefs. For when I was trying this, a Friend 
coming to vifit me, I ftopp'd him at the Door, 
and before I told him what the Colours were, or 
what I was doing ; I asked him. Which of the 
two Whites were the beft, and wherein they dif- 
fered ? And after he had at that diflance viewed 
them well, he anfwer'd, that they were both good 
Whites, and that he could not fay which was 
beft, nor wherein their Colours differed. Now, 
if you confider, that this White of the Powder 
in the Sun-fliine was compounded of the Co- 
lours which the component Powders ( Orpi- 
ment. Purple, Bife, and Viride JEris ) have in 
the fame Sun-fhine, you muft acknowledge by 
this Experiment, as well as by the former, that 
perfedt Whitenefs may be compounded of Co- 
lours. 

From what has been faid it is alfo evident, 
that the Whitenefs of the Sun's Lisrht is com- 
pounded of all the Colours wherewirh the feve- 
ral forts of Rays whereof that Light confifts, 
when by their feveral Refrangibilities they are 

K 3 fepa- 



134 O P T I C K S. 

feparated from one another, do tinge Paper or any 
other white Body whereon they fall. For thofe 
Colours {hy Prop.ll. Part 2.) are unchangeable, 
and whenever all thofe Rays w^ith thofe their Co- 
lours are mix'd again, they reproduce the fame 
white Light as before. 



PROP. VI. Prob. II. 

Lt a mixture of Primary Colour s-^ the 
^luantity and S^uality of each bei7tg 
given^ to know theColour of the Compound, 

WITH the Center O [m Fig. 11.] and 
Radius OD defcribe a Circle ADF, and 
diltinguiih its Circumference into feven Parts 
DE, EF, FG, GA, AB, B C, CD, propor- 
tional to the feven Mufical Tones or Intervals 
of the eight Sounds, «So/, /^, fa^ fol^ la^ mi, fa, 
fol, contained in an eight, that is, proportional 
to the Number ~, 75, ts, |, 15, is, \. Let the firfl 
Part I>E reprefent a red Colour, the fecond E F 
orange, the third F G yellow, the fourth C A 
green, the fifth AB blue, the fixth BC indigo, 
and the feventh C D violet. And conceive that 
thefe are all the Colours of uncompounded Light 
gradually pafiing into one another, as they do 
when made by Prifms j the Circumference 
DEFGABCD, reprefenting the whole Series 
of Colours from one end of the Sun's colour'd 
Image to the other, fo that from D to E be 
all degrees of red, at E the m.ean Colour be- 
tween red and orange, from E to F all de- 
crees 



B O O K I. 135 

grees of orange, at F the mean between orange 
and yellow, from F to G all degrees of yellow, 
and fo on. Let p be the Center of Gravity 
of the Arch D E, and q^ r, j, t, u^ Xy the Cen- 
ters of Gravity of the Arches E F, F G, G A, - 
A B, B C, and C D refpedively, and about 
thofe Centers of Gravity let Circles proportio- 
nal to the Number of Rays of each Colour in 
the given Mixture be defcrib'd ; that is, the 
Circle p proportional to the Number of the 
red-making Rays in the Mixture, the Circle q 
proportional to the Number of the orange-ma- 
king Rays in the Mixture, and fo of the reft. 
Find the common Center of Gravity of all thofe 
Circles p, q^ r, s, t, z/, x. Let that Center be 
Z; and from the Center of the Circle ADF, 
through Z to the Circumference, drawing the 
Right Line O Y, the Place of the Point Y in the 
Circumference Ihall ihew the Colour arifmg from 
the Compofition of all the Colours in the given 
Mixture, and the Line OZ fhall be propor- 
tional to the Fulnefs or Intenfenefs of the 
Cok)ur, that is, to its diftanCe from Vv^iitenefs. 
As if Y fall in the middle between F and G, 
the compounded Colour fliall be the beft yel- 
low J if Y verge from the middle towards F 
or G, the compound Colour fliall accordingly 
be a yellow, verging towards orange or green. 
If Z fall upon the Circumference, the Colour 
fhall be intenfe and florid in the higheft Degree ; 
if it fall in the mid- way between the Circum- 
ference and Center, it fhall be but half fo 
intenfe, that is, it fhall be fuch a Colour as 
would be made by diluting the intenfeil yellow 

K 4 with 



136 O P T I C K S. 

with an equal quantity of whitenefs ; and if it 
fall upon the center O, the Colour fhall have loft 
all its intenfenefs, and become a white. But it 
is to be noted, That if the point Z fall in or 
near the line OD, the main ingredients being 
the red and violet , the Colour compounded 
fhall not be any of the prifmatick Colours, but 
a purple, inclining to red or violet, according- 
ly as the point Z lieth on the fide of the line 
DO towards E or towards C, and in general 
the compounded violet is more bright and more 
fiery than the uncompounded. Alfo if only two 
of the primary Colours which in the circle are 
pppofite to one another be rnixed in an equal 
proportion, the point Z {hall fall upon the cen- 
ter O, and yet the Colour compounded of thofe 
two fhall not be perfectly white , but fome 
faint anonymous Colour, For I could never 
yet by mixing only two primary Colours pro- 
duce a perfeft white. Whether it may be com- 
pounded of a mixture of three taken at equal 
diftances in the circumference I do not know, 
but of four or five I do not much queftion but 
it may. But thefe are Curiofities of little or no 
moment to the underflanding the Phaenomena 
of Nature. For in all whites produced by Na- 
ture, there ufes to be a mixture of all forts of 
Rays, and by confequence a compofition of all 
Colours. 

To give an inftance of this Rule; fuppofe a 
Colour is compounded of rhefe homogeneal 
Colours, of violet one part, of indigo one part, 
of blue two parts, of gi^een three parts, of yel- 
)pw five parts, of orange fix parts, and of red 

ten 



B O O K I. 137 

ten parts. Proportional to thefe parts defcribe 
the Circles x, v, /, s, r, q, p, refpedively, that is, 
fo that if the Circle x be one, the Circle 1; may- 
be one, the Circle f two, the Circle s three, and 
the Circles r, q and/>, five, fix and ten. Then I 
find Z the common center of gravity of thefe 
Circles, and through Z drawing the Line OY, 
the Point Y falls upon the circumference between 
E and F, fomething nearer to E than to F, and 
thence I conclude, that the Colour compounded 
of thefe Ingredients will be an orange, verging a 
little more to red than to yellow. Alfo I find 
that OZ is a little lefs than one half of O Y, and 
thence I conclude, that this orange hath a little 
lefs than half the fulnefs or intenfenefs of an un- 
compounded orange j that is to fay, that it is 
fuch an orange as may be made by mixing an ho- 
mogeneal orange with a good white in the pro- 
portion of the Line OZ to the Line ZY, this 
Proportion being not of the quantities of mixed 
orange and white Powders, but of the quantities 
of the Lights reflected from them. 

This Rule I conceive accurate enough for pra- 
dtice, though not mathematically accurate ; and 
the truth of it may be fufliciently proved to Senfe, 
by flopping any of the Colours at the Lens in the 
tenth Experiment of this Book. For the refi: of 
the Colours which are not fi:opp'd, but pafs on to 
the Focus of the Lens, will there compound 
either accurately or very nearly fuch a Colour, as 
by thi^ Rule ought to refult from their Mixture. 

FRO P. 



138 O P T I C K S. 

PROP. VIL The OR. V. 

/ill the Colours in the Univerfe which are 
made by Lights and depend not on the 
Power of Imagination^ are either the 
Colours of homogeneal Lights^ or com- 
founded of thefe-^ and that either accu- 
rately or very nearly^ according to the, 
Rule of the foregoing Problem, 

FOR it has been proved (in Frop. i. Fart 2.) 
that the changes of Colours made by Refra- 
d:ions do not arife from any new Modifications of 
the Rays imprefs'd by thofe Refradions, and by 
the various Terminations of Light and Shadow, 
as has been the conftant and general Opinion of 
Philofophers. It has alfo been proved that the 
feveral Colours of the homogeneal Rays do con- 
ftantly anfwer to their degrees of Refrangibility, 
[Prop. I. Part i. andPrc/^. 2. Part 2.) and that 
their degrees of Refrangibility cannot be changed 
by Refractions and Reflexions [Prop. 2. Part i.) 
and by confequence that thofe their Colours 
are likewife immutable. It has alfo been pro- 
ved diredlly by refrafting and reflecting homo- 
geneal Lights apart, that their Colours cannot be 
changed, [Prop. 2. Part 2.) It has been proved 
alfoj that when the feveral forts of Rays are mix- 
ed, and in croflmg pafs through the fame'fpace, 
they do not ad- on one another fo as to change 
each others colorific qualities. [Exper. 10. Part 2.) 
but by mixing their Adions in the Senforium be- 
get 



BOOK I. 139 

get a Senfation differing from what either would 
do apart, that is a Senfation of a mean Colour 
between their proper Colours j and particularly 
when by the concourfe and mixtures of all forts 
of Rays, a white Colour is produced, the white 
is a mixture of all the Colours which the Rays 
would have apart, [Frop. 5. Part 2.) The Rays 
in that mixture do not lofe or alter their feveral 
colorific qualities, but by all their various kinds 
of Adions mix'd in the Senforium, beget a Sen- 
fation of a middling Colour between all their Co- 
lours, which is whitenefs. For whitenefs is a 
mean between all Colours, having it felf indiffe- 
rently to them aU, fo as with equal facility to be 
tinged with any of them. A red Powder mixed 
with a little blue, or a blue with a little red,' doth 
not prefcnrly lofe its Colour, but a white Powder 
mix'd with any Colour is prefently tinged with 
that Colour, • and is equally capable of being 
tinged with any Colour whatever. It has been 
fhewed alfo, that as the Sun's Light is mix'd of 
all forts of Rays, fo its whitenefs is a mixture of 
the Colours of all forts of Rays -, thofe Rays ha- 
ving from the beginning their feveral colorific 
qualities as well as their feveral Refrangibilities, 
and retaining them perpetually unchanged not- 
withftanding any Refradtions or Reflexions they 
may at any time fuffer, and that whenever any 
fort of the Sun's Rays is by any means (as by 
Reflexion in Exper. g. and 10. Part i. or by 
Refradion as happens in all Refractions) fepara- 
ted from the reft, they then manifell; their proper 
Colours. Thefe things have been prov'd, and 
the fujn of all this amounts to the Propofitioa 

here 



I40 O P T I C K S. 

here to be proved. For if the Sun's Light is 
mix'd of feveral forts of Rays, each of which 
have originally their feveral Refrangibilities and 
colorific Qualities, andnotwithftanding their Re- 
.fraftions and Reflexions, and their various Sepa- 
rations or Mixtures, keep thofe their original 
Properties perpetually the fame without alterati- 
on ; then all the Colours in the World muft be 
fuch as conftantly ought to arife from the origi- 
nal colorific qualities of the Rays whereof the 
Li2;hts confift by which thofe Colours are feen. 
And therefore if the reafon of any Colour what- 
ever be required, we have nothing elfe to do than 
to confider how the Rays in the Sun's Light have 
by Reflexions or Refraftions, or other caufes, been 
parted from one another, or mixed together j or 
otherwfe to find out what forts of Rays are in the 
Light by which that Colour is made, and in what 
Proportion ; and then by the laft Problem to 
learn the Colour which ought to arife by mixing 
thofe Rays (or their Colours) in that proportion. 
I fpeak here of Colours fo far as they arife from 
Light. For they appear fometimes by other Cau- 
fes, as when by the power of Phantafy wc fee Co- 
lours in a Dream, or a Mad-man fees things be- 
fore him which are not there; or when we fee 
Fire by flriking the Eye, or fee Colours like the 
Eye of a Peacock's Feather, by prefTing our Eyes 
in either corner whilft we look the other way. 
Wliere thefe and fuch like Caufes interpofe nor, 
the Colour always anfwers to the fort or forts 
of the Rays whereof the Light confifts, as I 
have conftantly found in whatever Phasnomena of 
Colours I have hitherto been able to examine. 

I aiall 



B O O K I. 141 

I {hall in the following Proportions give inftan- 
ces of this in the Phaenomena of chiefeft note. 



PROP, VIII. Prob. III. 

By the difcove7'ed Properties of Light to 
explain the Colours made by Prijms. 

LET ABC [in Fig. 12.] reprefent a Prifnl 
refracting the Light of the Sun, which 
comes into a dark Chamber through a hole F <j> 
almofl as broad as the Prifm, and let M N re- 
prefent a white Paper on which the refracted 
Light is caft, and fuppofe the moil refrangible 
or deepeft violet-making Rays fall upon the 
Space Pttj the leaft refrangible or deepeft red- 
making Rays upon the Space T7, the rniddle, 
fort between the Indigo-making and blue-mu- 
king Rays upon the Space Qv, the middle fort 
of the green-making Rays upon the Space Rp, 
the middle fort between the yellow-making and 
orange-making Rays upon the Space S a-, and o- 
ther intermediate forts upon intermediate Spa- 
ces. For fo the Spaces upon which the feveral 
forts adequately fall will by reafon of the diffe- 
rent Refrangibility of thofe forts be one lower 
than another. Now if the Paper MN be fo 
near the Prifm that the Spaces PT and ^-j do 
not interfere with one another, the diftance be- 
tween them T it will be illuminated by all the 
forts of Rays in that proportion to one another 
which they have at their very firft coming out 

of 



142 O P T I C K S. 

of the Prifm, and confequently be white. But 
the Spaces P T and ttT on either hand, will not 
be illuminated by them all, and therefore will 
appear coloured. And particularly at P, where 
the outmofl violet-making Rays fall alone, the 
Colotir mufi: be the deepeft violet. At Q^here 
the violet-making and indigo-making Rays are 
mixed, it mufl: be a violet inclining much to 
indigo. At R where the violet-making, indigo- 
making , blue-making , and one half of the 
green-making Rays are mixed , their Colours 
muft (by the conftrudtion of the fecond Pro- 
blem ) compound a middle Colour between in- 
digo arid blue. At S where all the Rays are 
mixed, except the red-making and orange-ma- 
king, their Colours ought by the fame Rule to 
compound a faint blue, verging more to green 
than indigo. And in the progrefs from S to T, 
this blue will grow more and more faint and' 
dilute, till at T, where all the Colours begin to 
be mixed, it ends in whitenefs. ^ 

So again, on the other fide of the white at r, 
where the leaft refrangible or utmoft red-ma- 
king Rays are alone, the Colour mull: be the 
deepeft red. At a the mixture of red and o- 
range will compound a red inclining to orange. 
At ^ the mixture of red, orange, yellow, and 
one half of the green muft compound a middle 
Colour between orange and yellow. At ^ the 
mixture of all Colours but violet and indigo will 
compound a faint yellow, verging more to green 
than to orange. And this yellow will grow 
more faint and dilute continually in its progrefs 

from 



B O O K I. 143 

from V to TT, where by a mixture of all forts of 
Rays it will become white. 

Thefe Colours ought to appear were the Sun*s 
Light perfedly white: But becaufe it inclines to 
yellow, the Excefs of the yellow-making Rays 
whereby 'tis tinged with that Colour, being 
mixed with the faint blue between S and T, will 
draw it to a faint green. And fo the Colours In 
order from P to r ought to be violet, indigo, 
blue, very faint green, white, faint yellow, o- 
range, red. Thus it is by the computation : And 
they that pleafe to view the Colours made by a 
Prifm will find it fo in Nature. 

Thefe are the Colours on both fides the white 
when the Paper is held between tlie Prifm and 
the Point X where the Colours meet, and the 
interjacent white vaniflies. For if the Paper be 
held flill farther off from the Prifm, the mofl 
refrangible and leaft refrangible Rays will be 
wanting in the middle of the Light, and the refl . 
of the Rays which are found there, will by mix- 
ture produce a fuller green than before. Alfo 
the.yellowand blue will now become lefs com- 
pounded, alid by confequence more intenfe than 
before. And this alfo agrees with experience. 

And if one look through a Prifm upon a 
white Objed: cncompafTed with blacknefs or 
darknefs, the reafon of the Colours arifing on 
the edges is much the fame, as will appear to 
ons that fhall a little confider it. If a black Ob- 
jed: be encompafTed with a white one, the Co- 
lours which appear through the Prifm are to be 
derived from the Light of the white one, fpread- 
ing into the Regions of the black, and therefore 

they 



144 O P T I C K S. 

they appear in a contrary order to that, when a 
white Objeft is furrounded with black. And the 
fame is to be underftood when an Obje6l is view- 
ed, whofe parts are fome of them lefs luminous 
than others. For in the borders of the more and lefs 
luminous Parts, Colours ought always by the fame 
Principles to arife from the Excefs of the Light 
of the more luminous, and to be of the fame 
kind as if the darker parts were black, but yet to 
be more faint and dilute. 

What is faid of Colours made by Prifms may 
be eafily applied to Colours made by the GlalTes 
of Telefcopes or Microfcopes, or by the Hu- 
mours of the Eye. For if the Objedl-glafs of 
a Telefcope be thicker on one fide than on the 
other, or if one half of the Glafs, or one half 
of the Pupil of the Eye be cover'd with any 
opake fubftance j the Objedi-glafs, or that part of 
it or of the Eye which is not cover'd, may be 
confider'd as a Wedge with crooked Sides, and 
* every Wedge of Glafa or other pellucid Subftance 
has the effect of a Prifm in refradiing the Light 
which paffes through it *. 

How the Colours in the ninth and tenth Ex- 
periments of the lirfl Part arife from the diffe- 
rent Reflexibility of Light, is evident by whar 
was there faid. But it is obfervable in the ninth 
Experiment, that whilft the Sun's dired: Light 
is yellow, the Excefs of the blue-making Rays 
in the refleded beam of Light MN, fuffices 
only to bring that yellow to a pale white incli- 
ning to blue, and not to tinge it with a mani- 

* See eur AuthorV Left. Optic. Part II. Se^. II. fa^. i6g, &(. 

feftly 



B Q O K I. 145 

feftly blue Colour. To obtain therefore a better 
blue, I ufed inftead of the yellow Light of the 
Sun the white Light of the Clouds^ by varying a 
little the Experiment, as follows. 

Exper, 16. Let HFG [in Fig. 13.] repre- 
fent a Prifm in the open Air, and S the Eye of 
the Spedator, viewing the Clouds by their 
Light coming into the Prifm at the Plane Side 
FIGK, and refleded in it by its Bafe HEIG, 
and thence going out through its Plane Side 
H E F K to the Eye. And when the Prifm and 
Eye are conveniently placed, fo that the Angles 
of Incidence and Reflexion at the Bafe may be 
about 40 Degrees, the Spe£latpr will fee a Bow 
MN of a blue Colour, running from one End 
of the Bafe to the other, with the Concave Side 
towards him, and the Part of the Bafe IMNG 
beyond this Bow will be brighter than the other 
Part E M N H on the other Side of it. This blue 
Colour M N being made by nothing elfe than by 
Reflexion of a fpecular Superficies, feems fo odd 
a Phaenomenon, and fo difficult to be explain- 
ed by the vulgar Hypothefis of Philofophers, 
that I could not but think it deferved to be taken 
Notice of. Now for underftanding the Rea- 
fgn of it, fuppofe the Plane. ABC to cut the 
Plane Sides and Bafe of the Prifm perpendicu-r 
larly. From the Eye to the Line B C, wherein 
that Plane cuts the Bafe, draw the Lines S^ 
and S/', in the Angles S^^: 50 degr. i, and Stc 
49 degr. Vt, and the Point p will he the Limit 
beyond which none of the moft refrangible 
Rays can pafs through the Bafe of the Prifm, 
and be refraded, whofe Incidence is fuch thai; 

L t'hey 



14,6 OPTIC K S. 

they may be refieded to the Eye ; and the Point 
t will be the like Limit for the leaft refrangi- 
ble. Rays, that is, beyond which none of them 
can pafs through the Bafe, whoie Incidence is 
fuch that by Reflexion they may come to the 
Eye. . And the Point r taken in- the middle 
Way betv/een p and ^, will be the like Limit 
for the meanly . refrangible Rays. And there- 
fore all the leaft refrangible Rays which fall 
upon the Bafe beyond /, that is, between t and B, 
and can come from thence to the Eye, will be 
refledted thither : But on this fide t^ that is, 
between t and f, many of thefe Rays will be 
tranfmitted through the Bafe. And all the moft 
refrangible Pvays which fall upon the Bafe be- 
yond ^, that is, between p and B, and can by 
Reflexion come from thence to the Eye, will be 
refleded thither, but every where between p 
and r, many of thefe Rays will get through the 
Bafe, and be refraded j and the fame is to be 
underftood of the meanly refrangible Rays on 
either fide of the Point r. Whence it follows, 
that the Bafe of the Prifm rriufl every where 
between t and B, by a total Reflexion of all forts 
of Rays to the Eye, look white and bright. 
And every where between p and C, by reafon of 
the Tranfmiflion of many Rays of every fort, 
look more pale, obfcure, and dafk. But at r, 
and in other Places between p and /, where all 
the more refrangible Rays are refledied to the 
Eye, and many of the lefs refrangible are. tranf- 
.mitted, the Excefs of the moft refrangible in 
the refleded Light will tinge that Light with 
their Colour, which is violet and blue. Arid- 

this 



B O O K I. 147 

this happens by taking the Line C/r/B any 
.where between the Ends of the Prilm H G 
and EI. 



PROP, IX. prob. r\^. 

By the difcGvered Pf'operties of Lighi to 
explain the Colours of the Rain-bow, 

THIS Bow never appears, but where it 
n|ins in the Sun-fhine, and may be made 
artiticially by fpouting up Water which may 
break aloft, and fcatter into Drops, and fall down 
like Rain. For the Sun fliining upon thefe 
Drops certainly caufes the Bow to appe^f* to a 
Spectator ftanding in a due Polition to the Rain 
and Sun. And hence it is now agreed upon, 
that this Bow is made by Refraction of the Sun's 
Light in Drops of falling Rain. This^was un- 
derllood by fome of the Antients, and of late 
more fully difcover'd and explain'd by the fa- 
mous Antoniiis de Dominis Archbilhop of ^pa- 
lato, in his Book De Radiis Visits & Liicis, pub- 
lifhed by his Friend Bartolus at Venice^ in the 
Year 161 1,. and written above 20 Yeai's before. 
For he teacher' there how the interior Bow is 
made in round Drops of Raiii by two Refracti- 
ons of the Sun's Light, and one Reflexion be- 
tween them, and the exterior by two Refradti- 
ons, and two forts of Reflexions between them 
in each Drop of Vv^ater, and proves his Expli- 
cations by Experiments made witba Phial full 
lof Water, and with Globes of Glafs filled 

L 2 with 



148 O P T I C K S. 

with Water, and placed in the Sun to make the 
Colours of the two Bows appear in them. The 
fame Explication Des-Cartes hath purfued in his- 
Meteors, and mended that of the exterior Bow. 
But whilft they underftood not the true Ori- 
gin of Colours, it's neceffary to purfue it here 
a little farther. For underftanding therefore how 
the Bow is made, let a Drop of Rain, or any 
other fpherical tranfparent Body be reprefented 
by the Sphere BNFG, [in Fig. 14.] defcribed 
with the Center C, and Semi-diameter C N. 
And let AN be one of the Sun's R^s inci- 
dent upon it at N, and thence refradled to F, 
where let it either go out of the Sphere by Re- 
fraction towards V, or be refle<5ted to G ; and 
at G " let it either go out by Refradion to R, or 
be refledled to H; and at H let it go out by 
Refrad:ion towards S, cutting the incident Ray 
in Y. Produce AN and RG, till they meet in 
X, and upon AX and NF, let fall the Per- 
pendiculars CD and CE, and produce CD till 
it fall upon the Circumference at L. Parallel to 
the incident Ray AN draw the Diameter B Q^ 
and let the Sine .of Incidence out of Air into 
Water be to the Sine of Refradion as I to R. 
Now, if you fuppofe the Point of Incidence N 
to move from the Point B, continually till it 
come to L, the Arch Q F will firil increafe and 
then decrcafe, and fo will the Angle A X R 
which the Rays A N and G R contain ; and the 
Arch QJ' and Angle AXR w ill be biggeft 
when ND is to CN as -/H^RR to v/ 3 RR, in 
which cafe NE will be to ND as 2 R to I. Alfo 
the Angle AYS, which the Rays AN and HS 

contain 



B O O K I. 149 

contain will firft decreafe, and then increafe and 
grow leaft when ND is to CN as y'llZlRK to 
^8RR, in which cafe NE will be to ND, as 
3 Rtol. And fo the Angle which the next emer- 
gent Ray ( that is, the emergent Ray after three 
Reflexions) contains with tlie incident Ray AN 
will come to its Limit when ND is to CN 
as y/li— KR to / 15 RR, in which cafe NE will 
be to N D as 4 R to I. And the Angle which the 
Ray next after that Emergent, that is, the Ray 
emergent after four Reflexions, contains with the 
Incident, will come to its Limit, when N D is to 
CN as /ii — KK to v/ 24 RR, in which cafe NE 
will be to ND as 5 R to I i and fo on infinitely, 
the Numbers 3,8, 15, 24, &c. being gather'd by 
continual Addition of the Terms of the arithme- 
tical Progreflion 3, 5, 7, 9, ^c. The Truth of all 
this Mathematicians will ealily examine.* > . 

Now it is to be obferved, that as when the Sun 
comes to his Tropicks, Days increafe and decrcafe 
but a very little for a great while together j fo when 
by increaling the diflance CD, thefe Angles come 
to their Limits, they vary their quantity but very 
little for fome time together, and therefore a fir 
greater Number of the Rays which fill upon all 
the Points N in the Quadrant BL, {hall emcrg. in 
theLimits of thefe Angles, than in any other Incli- 
nations. And farther it is to be obferved, that the 
Rays which differ in Refrangibility will have dif- 
ferent Limits of their Angles of Emergence, and 
by confequence according to their different De^ 
grees of Refrangibility emerge moft copioufly 

_, * This is demonjirated in our Author'j Ledl. Optic Part I. Se^l. IV. 
Prop. 35 and 36. 

L 3 in 



150 O P T I C K S. 

in different Angles, and being feparated from one 
another appear each in their proper Colours, 
And v/hat thole Angles are may be eaiily ga- 
ther'd from the foregoing Theorem by Com- 
putation. 

For in the leaft refrangible Rays the Sines I 
and R (as was found above) are io8 and 8i, 
and thence by Computation the greateft Angle 
AXR will be found 42 Degrees and 2 Minutes, 
and the kail Angle AYS, 50 Degrees and c^j 
Minutes. And in the moll refrangible Rays the 
Sines I and R are 109 and 81, and thence by 
Computation the greateft Angle AXR wilh be 
found 40 Degrees and 17 Minutes, and the leaft 
Angle AYS 54 Degrees and 7 Minutes. 

Suppofe now \^\'^x. O [ in Fig. 15. ] is the Spe- 
6lator's Eve, and OP a Line drawn parallel to 
the. Sun's 'Rays, and let POE, POF, POG, 
POH, be Angles of 40 Degr. 17 Min. 42 Degr. 
2 Mm. 50 Degr. c^-j Min. and 54 Degr. 7 Min. 
refpe6tively, and thefe Angles turned about 
their common Side O P, fhall with their other 
Sides OE, OF; OG, OH, defcribe the Verges 
of two Rain-bows AF BE and CHDG. Foi* 
if E, F, G, H, be drops placed any where in 
the conical Superficies defcribed by OE, OF, 
OG, OH, and be illuminated by the Sun's Rays 
SE, SF, SG, SH; the Angle SEO being e- 
qual to the Angle POE, or 40 Degr. 17 Min. 
ihall be the greateft Angle in which the moft 
refrangible Rays can after one Pvetiexion be re- 
fradled to the Eye, and therefore all the Drops 
in the Line O E Inall fend the moft refrangible 
Rays moft copioufly to the Eye, and thereby 

ftrike 



BOO KllC fi5a 

i\nkt the ^fes with the deepeft violet Colour in 
that Region. And in like manner the^^ngle SFO 
being equal to the Angle POF, or 42 Degr. 
2 Min. fhall be the greateft in which the Icall: re- 
frangible Rays after one Reflexion can emerge 
out of the Drops, and therefore thofe Rays 
.fliall come moft copioufly to the Eye from the 
Drops in the Line O F, and flrike the Senfes with 
the deepeft red Colour in that Region. And by 
■the fame Argument, the Rays which have inter- 
mediate Degrees of Refrangibility fliall comeiinofl 
copioufly from Drops between E and F, and'llirike 
the Senies with the intermediate Colours, in the 
Order which their Degrees of Refrangibility rc- 
€|uiie, that is in the Progfefs 'from E toF, or 
from the infide of the Bow to the outfide in this 
order, violet, indigo, blue, green, ycllow,"^^ orange, 
red. But the violet, by the mixtiue of the white 
Light of the Clouds, will appear laint and in- 
cline to purple. 

- Again, the Angle SGO being equal to the 
Angfe POG, or 5oGr. 51 Min. fhall be the Iciift 
Angle in which the leaft refrangible Rays can 
after two Reflexions emerge out of the Drops, 
and therefore the leafl refrangible Rays lliall 
come moffc copioufly to the Eye from the Drops 
i-n the Line OG, and firike the StnfQ with the 
deepeft red in that Region. And the Angle 
SHO being equal to the Angle POH, or 54 Gr.- 
7 Min. fliall be the leafl Angle, in which the moft 
refrangible Rays after two Pvcfiexions can emerge 
out of the Drops J and therefore thofe Rays 
fhall come mofl copioufly to the Eye froni^ 
the Drops in the Line OFI, and ilrike the Senfes 

L 4 with 



152 O P T I C K S. 

with the deepeft violet in that Region. And by the 
fame Argument, the Drops in the Regions be- 
tween G and H fliall ftrike the Senfe with the in- 
termediate Colours in the Order which their 
Degrees of Refrangibility require, that is, in the 
Progrefs from G to H, or from the infide of the 
Bow to the outiide in this order, red, orange, yel- 
low, green, blue, indigo, violet. And fmce 
thefe four Lines OE, OF, OG, OH, may be 
■fituated any where in the above-mention'd co- 
iiical Superficies ; what is faid of the Drops 
and Colours in thefe Lines is to be underftood 
of the Drops and Colours every where in thofe 
Superficies. 

Thus iliall there be made tv^o Bows of Co- 
lours, an interior and ftronger, by one Reflexion 
jn the Drops, and an exterior and fainter by 
two J for the Light becomes fainter by every 
Reflexion. And their Colours fhall lie in a con- 
trary Order to one another, the red of both Bows 
bordering upon the Space GF, which is be- 
tween the Bows. The Breadth of the inte- 
rior Bow EOF meafured crofs the Colours fhall 
be I Degr. 45 Min. and the Breadth of the ex- 
terior GOH fhall be 3 Degr. 10 Min. and the 
diflance between them GOF fhall be 8 Gr. 15 
Min. the greateft Semi-diameter of the inner- 
mofl, that is, the Angle POF being 42 Gr. 2 
Min. and the leafl Semi-diameter of the outer- 
mofl POG, being 50 Gr. 57 Min. Thefe are 
the Meafures of the Bows, as they would, be 
were the Sun but a Point ; for by the Breadth 
of his Body, the Breadth of the Bows will be in^ 
creafed, and ^heir Diflance decreafed by half a 

Degree,' 



B O O K I. 153 

Degreq, and (o the breadth of the interior Iris 
will be 2 Degr. J5 Min. that of the exterior 3 
Degr. 40 Min. their diftance 8 Degr. 25 Min. 
the greateft Semi-diameter of the interior Bow 
42 Degr. 17 Min. and the leail of the exterior 
50 Degr. 42 Min. And fuch are the Dimenfions 
of the Bows in the Heavens found to be very 
nearly, when their Colours appear ftrong and 
perfed:. For once, by fuch means as I then liad, 
I .meafured the greateft Semi-diameter of the 
interior Iris about 42 Degrees, and the breadth 
of the red, yellow and green in that Iris 63 or 
64 Minutes, befides the outmoft faint red ob- 
fcured by the brightnefs of the Clouds, for 
which we may allow 3 or 4 Minutes more. , The 
breadth of the blue was about 40 Minutes more 
belides the violet, .which was fo much obfcu- 
red by the brightnefs of the Clouds, that I could 
not meafure its breadth. But fuppofing the 
breadth of the blue and violet together to equal 
that of the red, yellow and green together, the 
whole breadth of this Iris will be about 2 t De- 
grees, as above. The leail diftance between this 
Iris and the exterior Iris was about 8 De2;rees and 
30 Minutes. The exterior Iris was broader than 
the interior, but fo faint, efpecially on the blue 
fide, that I could not meafure its breadth di- 
ftindlly. At another time when both Bows ap- 
peared more diftind:, I meafured the breadth of 
the interior Iris 2 Gr. 10', and the breadth of the 
red, yellow and green in the exterior Iris, was to 
the breadth of the fame Colours in the interior 
as 3 to 2. 

this 



154 O P T I C K S. 

This Explication of the Rain-bow is yet far- 
ther confirmed by the known Experiment (made 
by Antonius de Domini s and Des-Cartes ) of 
hanging up any where in the Sun-iliine a Glafs 
Globe filled with Water, and viewing it ih fuch 
a poflure, that the Rays which come from the 
Globe to the Eye may contain with the Sun's 
Rays an Angle of either 42 or 50 Degrees. ^ For 
if the Angle be about 42 or 43 Degrees, the 
Spectator ( fuppofe at O ) {hall fee a full i:ed 
Colour in that fide of the Globe oppofed to 
the Sun as 'tis reprefented at F, and if that An- 
^gle become lefs (fuppofe by depreflnig the Globe 
to E) there will appear other Colours, yellow, 
green and blue fucceflive in the fame fide of 
the Globe. But if the- Angle be made about 
50 Degrees (fuppofe by lifting up the Globe to 
G) there will appear a red Colour in that Me 
of the Globe towards the Sjun, and if the An- 
gle be made greater (fuppofe by lifting up tlie 
Globe to H) the red will turn fucceffively to 
the other Colours, yellow, green and blue. The 
fame thing I have tried, by letting a Globe reft, 
and raifing or depreifing the Eye , or other- 
wife moving it to make the Angle of ajufl mag* 
nitude. ;u y-. 

I have heard it reprefented, that if the Light 
of a Candle be refraded by a Prifm to the Eye ; 
when the blue Colour falls upon the Eye, the 
Spe<5tator {hall fee red in the Prifm, and when 
the red falls upon the Eye he fhall fee blue ; 
and if this were certain , the Colours of . the 
Globe and Rain-bow ought to appear in a. con- 
nary order to what we find. But the Colours 
^ of 



BOOK I. 155 

of the Candle being very faint, the miftake feems 
to arife from the difficulty of difcerning what 
Colours fall on the Eye. For, on the contrary, 
I have fometimes had occafion to obferve in the 
Sun's Light refraded by a Prifm, that the Spe- 
ctator always fees that Colour in the Prifm which 
falls upon his Eye. And the fame I have found 
true alfo in Candle-light. For when the Prifm 
is moved (lowly from the Line which is drawn 
diredly from the Candle to the Eye, the red ap- 
pears firft in the Prifm and then the blue, and 
therefore each of them is feen when it falls upon 
the Eye. For the red pafTes over the Eye firft, 
and then the blue. 

The Light which comes through drops of 
Rain by two Refra6tions without any Reflexion, 
ought to appear ftrongeft at the diftance of a- 
bout. 26- Degrees from the Sun, and to decay 
gradually both ways as the diftance from him in- 
creafes and decreafes. And the fame is to be un- 
derftood of Light tranfmitted through fphe- 
"rical Hail-ftones. And if the Hail be a little 
flatted , as it often is , the Light tranfmitted 
may grow fo ftrong at a little lefs diftance than 
that of 26 Degrees, as to form a Halo about 
the Sun or Moon ; which Halo, as often as the 
Hail-ftones are duly figured may be colour'd, 
and then it muft be red within by the leaft re- 
frangible Rays, and blue without by the moft 
refrangible ones, efpecially if the Hail-ftones 
have" opake Globules of Snow in their center 
to intercept the Light within the Halo {asHu^ 
genius has obferv'd) and make the infide there- 
of more diftind')y defined than it would other- 
wife 



156 O P T I C K S. 

wife be. For fuch Hail-ftones, though fpheri- 
cal, by terminating the Light by the Snow, 
may make a Halo red within and colourlefs 
without, and darker in the red than without, 
as Halos ufed to be. For of thole Rays which 
pafs clofe by the Snow the Rubriform will be 
ieaft refracted, and fo come to the Eye in the di- 
refteft Lines. 

The Light which pafTes through a drop of 
Rain after two Refra6:ions, and three or more 
Reflexions, is fcarce ftrong enough to caufe a 
fenfible Bow; but in thofe Cylinders of Ice by 
which Hiigenius explains the Parhelia^ it may 
perhaps be fenfible. 



PROP. X. Prob. V. 
By the difccvered Properties of Light to 
explain the permanent Colours of Natu- 
ral Bodies, 

THESE Colours arife from hence , that 
fome natural Bodies refled: fome forts of 
Rays, others other forts more copioufly than the 
reft. Minium refledts the Ieaft refrangible or 
red-rfiaking Rays moft copioufly, and thence ap- 
pears red. Violets refled: the moft refrangible 
moft copioufly, and thence have their Colour, 
and fo of other Bodies. Every Body refledls the 
Rays of its own Colour more copioufly than the 
reft, and from their excefs and predominance in 
the refleded Light has its Colour. 

Exper^ 



B O O K I. 157 

Exper. ij. For if in the homogeneal Lights 
obtained by the folution of the Problem pro- 
pofed in the fourth Propolition of the firft Part 
of this Book, you place Bodies of feveral Co- 
lours, you will find, as I have done, that every 
Body looks mofl fpiendid and luminous in the 
Light of its own Colour. Cinnaber in the ho- 
mogeneal red Light is mofl refplendent, in the 
.green Light it is manifeftly lefs refplendent, and 
in jhe blue Light ftill lefs. Lidigo in the vi- 
olet blue Light is moll refplendent, and its fplen- 
dor is gradually diminiih'd, as it is removed 
thence by degrees through the green and yellow 
Light to the red. By a Leek the green Light, 
and next that the blue and yellow which com- 
pound green, are more flrongly refle6ted than the 
other Colours red and violet, and fo of the reft. 
But to make thefe Experiments the more mani- 
feft, fuch Bodies ought to be chofen as have the 
fulleft and moft vivid Colours, and two of thofe 
Bodies are to be compared together. Thus, for 
inftance, if Cinnaber and ultra-nMxv'mt blue, or 
fome other full blue be held together in the red 
homogeneal Light, they will both appear red, 
but the Cinnaber will appear of a ftrongly lumi- 
nous and refplendent red , and the ultra-mz- 
rine blue of a faint obfcure and dark red ; and 
if they be held together in the blue homogeneal ' 
Light, they will both appear blue, but the ultra- 
marine will appear of a ftrongly luminous and 
refplendent blue, and the Cinnaber of a faint 
and dark blue. Which puts it out of difpute, 
that the Cinnaber reflecfts the red Light much 
more copioufly than the ////n;-marine doth, and 
2 the 



158 O P T I C K S. 

the ulfra-m^i'lne refleds the blue Light much 
more copioully than theCinnaber doth. The fame 
Experiment may be tried fuccefsfully with red 
Lead and Indigo, or with any other two colour'd 
Bodies, if due allowance be made for the diffe- 
rent ftrength or wealoiefs of their Colour and 
Light. 

And as the reafon of the Colours of natural 
Bodies is evident by thefe Experiments, fo it is. 
farther confirmed and put pafl difpute by ,the 
two firft Experiments of the firft Part, where- 
by 'twas proved in fuch Bodies that the reflefed 
Lights which differ in Colours do differ alfo in 
degrees of Refrangibility.^ For thence it's cer- 
tain, that fome Bodies reflect the more refran- 
gible, others the lefs refrangible Rays more co- 
piouily. 

And that this is not only a true reafon of thefe 
Colours, but even the only reafon, may appear 
farther from this Confideration, that the Colour 
of homogeneal Light cannot be changed by the 
Reflexion of natural Bodies. 

For if Bodies by Reflexion cannot in the leafl 
change the Colour of any one fort of Rays, they 
cannot appear colour'd by any other means than 
by refle(^ting thofe which either are of their 
own Colour, or which by mixture muft pro- 
duce it. 

But in trying Experiments of this kind care 
muft be had that the Light be fufficiently ho- 
mogeneal. For if Bodies be illuminated by the 
ordinary prifmatick Colours, they will appear 
neither of their own Day-light Colours, nor of 
the Colour of the Light caft on them, but of 

fome 



BOOK!. 159 

feme middle Colour between both, as I have 
found by Experience. Thus red Lead (for in- 
ftance ) illuminated with the ordinary prifma- 
"tick green will not appear either red or green, 
but orange or yellow, or between yellow and 
green, accordingly as the green Light by which 
'tis illuminated is more or lefs compounded. 
For becaufe red Lead appears red when illumi- 
nated with white Light , wherein all forts of 
Rays are equally mix'd, and in the green Light 
all forts of Rays are not equally mix'd, the Lx- 
cefs of the yellow-making , green-making and 
blue-making Rays in the incident green Light,' 
will caufe thofe Rays to abound fo niuch in the 
refle<^ted Light, as to draw the Colour from red 
towards their Colour. And becaufe the red Lead 
refle(fts the red-making Rays moft copioufly in 
proportion to their number, *and next after them 
the orange-making and yellow-making Rays ; 
thefe Rays in the refledted Light will be more in 
proportion to the Light than they were in the in- 
cident green Light, and thereby will draw the 
refleded Light from green towards their Co- 
lour. And therefore the red Lead will appear 
neither red nor green, but of a Colour between 
both. 

In tranfparently colour'd Liquors 'tis obfer- 
vable, that their Colour ufes to vary with their 
thicknefs. Thus, for inftance, a red Liquor in 
a conical Glafs held between the Light and the 
Eye, looks of a pale and dilute yellow at the 
bottom where 'tis thin, and a little higher where 
'tis thicker grows orange, and where 'tis ftili 
thicker becomes red, and where 'tis thickeft 

V the 



i6o O P T I C K S. 

the red is.deepefl anddarkeft. For it is to be 
conceiv'd that fuch a Liquor flops the indigo- 
making and violet-making Rays moft eafily, the 
blue-making Rays more difficultly, the green-' 
making Rays ftill more difficultly, and the red- 
making moft difficultly : And that if the thick- 
nefs of the Liquor be only fo much as fuffices 
to Hop a competent number of the violet-ma- 
king and indigo-making Rays, without dimi- 
nifliing much the number of the reft, the reft 
muft (by Prop. 6. Part 2.) compound a pale 
yellow. But if the Liquor be fo much thicker 
as to ftop alfo a great number of the blue-ma- 
king* Rays, and fo^ie of the ^reen-making, the 
reft muft compound an orange j and where it is 
fo thick as to ftop alfo a great number of the 
green-making and a confiderable number of the 
yellow-making, the I'eft muft begin to compound 
a red, and this red muft grow deeper and darker 
as the yellow-making and orange-making Rays 
are more and more ftopp'd by increafmg the 
thicknefs of the Liquor, fo that few Rays befides 
the red-making can get through. • 

Of this kind is an Experiment lately related 
to me by Mr. Halley, who, in diving deep , into 
the Sea in a diving Veftel, found in a clear Sun- 
fhine Day, that when he was funk many Fa- 
thoms deep into the Water, the upper part of 
his Hand on which the Sun ftione dired:ly 
through the Water and through a fmall Glafs 
Window in the Vefiel appeared of a red Co- 
lour, like that of a Damask Rofe, and the Wa- 
ter below and the under part of his Hand 
illuminated by Light refleded from the Water 

below 



BOOK I. i6i 

below look'd green. For thence it may be ga- 
ther'd, that the Sea- Water refleds back the violet 
and bhie-making Rays moft eafily, ,and lets the • 
red-making Rays pafs moft freely and copioufly to 
ffreat Depths. For thereby the Sun's direct Light 
at all great Depths, by reafcn of the predomi- 
nating red-making Rays, muft appear red j and 
the greater the Depth is, the fuller and in- 
tenfer muft that red be. And at fuch Depths 
as the violet-making Rays fcarce penetrate unto, 
the blue-making, green-making, and yellow- 
making Rays being refleded from below more 
copioully than the red-making ones, muft com- 
pound a green. 

Now, if there be two Liquons of full Colours, 
fiif)pofe a red and a blue, and both of them fo 
thick as fuffices to tnake their Colours fufficiently 
full; though either Liquor be fufficiently tranfpa- 
tenz apart, yet will you not bfe able to fee through 
Doth together. For, if only the red-making Rays 
pafs through one Liquor, arid only the blue* 
making through the other, no 'Rays can pafs 
through both. This Mr. H^ok' tried cafuilly 
^ith Glafs Wedges filled with red and blue Li- 
quors, and was furprized at the unexpeded Event, 
the reafon of it being then unknown ; which 
makes me truft the more to his Experiment, 
though I have not tried it my felf. But he 
that would repeat it, muft take care the Li- 
quors be of very good and full Colours. 

Now, whilft Bodies become coloured by refled:- 
ing or tranfmitting this or that fort of Rays more 
eopiouily than the reft, it is to be conceived that 
they ftop and ftrfle in themfelves the Rays 

M > which 



i62 O P T I C K S. 

which they do not refledt or tranfmit. For, if 
Gold be foliated and held between your Eye and 
. the Light, the Light looks of a greenifh blue, 
and therefore mafTy Gold lets into its Body the 
blue-making Rays to be reflected to and fro 
within it till they be ftopp'd and ftifled, whilft 
it refle(5ls the yellow-making outwards, and 
thereby looks yellow. And much after the fame 
manner that Leaf Gold is yellow by refle<ited, 
and blue by tranfmitted Light, and maify Gold 
.is yellow in all Pofitions of the Eye -, there are 
foqie Liqi:jors, as the Tincfture of Lignum 
Nephriticumy and fome forts of Glafs which 
tranfmit one fort of Light moft copioufly, and 
refled another fort, and thereby look of feve- 
4^al Colours, according to the Pofition of the 
Eye to the Light. But, if thefe Liquors or 
.Glafles were fo thick and mafTy that no Light 
could get through them, I queftion not but they 
fwould like all other opake Bodies appear or 
ohe and the fame Colour in all Pofitions of the 
Eye, though this I cannot yet affirm by Expe^ 
rience. For all colour'd Bodies, fo far as my 
Obfervation reaches, may be feen through if 
made fufficiently thin, and therefore are in fome 
meafure tranfparent, and differ only in degrees 
of Tranfparency from tinged tranfparent Li- 
<juors; thefe Liquors, as well as thofe Bodies, 
by a fufficient Thicknefs becoming opake. A 
tranfparent Body which looks of any Colour by 
tranfmitted Light, may alfo look of the fame 
Colour by reflected Light, the Light of that 
Colour being reflected by the farther Surface 
of the Body, or by the Air beyond it. And 

then 



BOOK L .161 

then the refleded Colour will be diminlfhed, and 
perhaps ceafe, by making the Body very thick, 
and pitching it on the backfide to diminifh the 
Reflexion of its farther Surface, fo that the Light 
refle(3;ed from the tinging Particles may predomi- 
nate. In fuch Cafes, the Colour of the reflecfted 
Light will be apt to vary from that of the Light 
tranfmitted. But whence it is that tinged Bo- 
dies and Liquors refledt fome fort of Rays, and 
intromit or tranfmit other forts, fhall be faid in 
the next Book. In this Propofition I content my 
felf to have put it paft difpute, that Bodies have 
fuch Properties, and thence appear colour'd. 



PROP. XI. Prob. VI. 

By mixing colour d Lights to compound a 
beam of Light of the fa^ne Colour and 
Nature with a beam of the Su?is direEi 
Light y and therein to experience the 
Truth of the foregoing Propoftions, 

LET ABC abc [in Fif[. 16.] reprefent a 
Prifm, by which the Sun's Light let into 
a dark Chamber through the Hole F, may be 
refradted towards the Lens MN, and paint upon 
it at py q, r, j, and /, the ufual Colours vio- 
let, blue, green, yellow, and red, and let the 
diverging Rays by the Refrad:ion of this Leng 
converge again towards X, and there, by the 
mixture of all thofe their Colours, compound a 
white according to what was fhewo above. 

M 2 Then 



i64 OPTIC K S. 

Then let another Prifm DEG deg, parallel to 
the former, be placed at X, to refrad: that white 
Light upward* towards Y. Let the refracting, 
Angles of the Prifms, and their diflances from 
the Lens be equal, fo that the Rays which con- 
verged from the Lens towards X, and without 
Refradion, would there have crofled and di- 
verged again, may by the Refradtion of the fe- 
cond Prifm be reduced into Parallelifm and 
diverge no more. For then thofe Rays will re- 
compofe a beam of white Light XY. If the 
refradting Angle of either Prifm be the bigger, 
that Prifm muft be fo much the nearer to the 
Lens. You will know when the Prifms and the 
Lens are well fet together, by obferving if the 
beam of Light X Y, which comes out of the fe- 
cond Prifm be perfectly white to the very edges 
of the Light, and at all diftances from the Prifm 
continue perfectly and totally white like a beam 
of the Sun's Light. For till this happens, the 
Polition of the Prifms and Lens to one another 
muft be correded ; and then if by the help ©f a 
long beam of Wood, as is reprefehted in the 
Figure, or by a Tube, or fbme other fuch In- 
ftrument made for that Purpofe, they- be made 
faft in that Situation, you may try all the fame 
Experiments in this compounded beam of Light 
X Y, which have been made in the Sun's dired: 
Light. For this compounded beam of Light 
has the fame appearance, and is endow'd with 
all. the fame Properties with a diredt beam of the 
Sun's Light, fo far as my Obfervation reaches. 
And in trying Experiments in this beam you 
may by flopping any of the Colours /, q^ r, /> 

and 



B O O K I. 165 

and /, at the Lens, fee how the Colours produce^ 
in the Experiments are no other than thofe which 
the Rays had at the Lens before they entered the 
Compofition of this Beam : And by confcqijence> 
that they arife not from any new Modifications of 
the Light by Refradtions and Reflexions, but from 
the various Separations and Mixtures of the Rays 
originally endow'd with theircolour-making Qua- 
lities. 

So, for inftance, having with a Lens 4, Liches 
broad, and two Prifms on either hand 6i Feet 
diftant from the Lens, made fuch a beam of 
compounded Light ; to examine the reafon of 
the Colours made by Prifms, I rcfraded this com- 
pounded beam of Light XY with another Prifm. 
HIK kh, and thereby call the ufual Prifma- 
tick Colours PQRST upon the Paper LV 
placed behind. And then by flopping any of 
the Colours />, ^, r, j, /, at the Lens, I found 
that the fame Colour would vanifh at the Pa- 
per. So if the Purple p was ftopp'd at the 
Lens, the Purple P upon the Paper would vanifh, 
and the reft of the Colours would remain un- 
alter'd, imlefs perhaps the blue, fo far as fome 
purple latent in it at the Lens might be fepa- 
rated from it by the following RefraSions. And 
fo by intercepting the green upon the Lens, the 
green R upon the Paper would vanifli, and fo 
of the refl j which plainly fhews, that as the 
white beam of Light XY was compounded of 
feveral Lights varioufly colour'd at the Lens, 
fo the Colours which afterwards emerge out of 
it by new Refradlions are no other than thofe 
of which its Whitenefs was compounded. The 

M 3 Refradion 



i66 O P T I C K S. 

Refradion of the Prifm HIK /^^ generates the 
Colours PQ^ST upon the Paper, not by chan- 
ging the colorific Qualities of the Rays, but by 
feparating the Rays which had the very fame colo- 
rific Qualities before they enter'd the Compofition 
of the refradied beam of white Light X Y. For 
otherwife the Rays which were of one Colour at 
the Lens might be of another upon the Paper, 
contrary to what we find. 

So again, to examine the reafon of the Co- 
lours of natural Bodies, I placed fuch Bodies 
in the Beam of Light XY, and found that they 
all appeared there of thofe their own Colours 
which they have in Day-light, and that thofe 
Colours depend upon the Rays which had the 
fame Colours at the Lens before they enter'd the 
Compofition of that beam. Thus, for inflance, 
Cinnaber illuminated by this beam appears of 
the fame red Colour as in Day-light ; and if 
at the Lens you intercept the green-making and 
blue-making Rays, its rednefs will become more 
full and lively : But if you there intercept the 
red-making Rays, it will not any longer ap- 
pear red, but become yellow or green, or of 
lome other Colour, according to the forts of 
Rays which you do not intercept. So Gold 
in this Light XY appears of the fame yellow 
Colour as in Day-light, but by intercepting at 
the Lens a due Quantity of the yellow-making 
Rays it will appear white like Silver ( as I have 
tried ) which Ihews that its yellownefs arifes from 
the Excefs of the intercepted Rays tinging that 
Whitenefs with their Colour when they are let 
pafs. So the Infuiion of Ugmm Nephriticum 

(as 



B O O K I. 167 

(as I have alfo tried) when held in this beam of 
Light XY, looks blue by the reflected Part of the 
Light, and red by the tranfrrjitted Part of it, as 
when 'tis view'd in Day-light j but if you intercepc 
the blue at the Lens the Infufion will lofe its re- 
fled:ed blue Colour, whilft its tranfmitted red re- 
mains perfect, and by the lofs of fome blue- 
making Rays, wherewith it was allay'd, becomes 
more intenfe and full. And, on the contrary, if 
the red and orange-making Rays be intercepted at 
the Lens, the Infufion will lofe its tranfmitted red, 
whilft its blue will remain and become more full 
and perfedl. Which fhews, that the Infufion 
does not tinge the Rays with blue and red, but 
only tranfmit thofe mofl copioufiy which were 
red-making before, and refledts thofe moft copi- 
oufly which were blue-making before. And after 
the fame manner may theReafons of other Phaeno- 
mena be examined, by trying thorn in this artificial 
beam of Light XY. 




M 4 THE 




THE 

SECOND BOOK 

OF 



OPTICKS. 



P A R T I. 



Obfervations concerning the Reflexions y Re- 
fraBionSy and Colours of thi^t tranfpa- 
rent Bodies, 



T has been obferved by others, 
that tranfparent Subftances, as 
Glafs, Water, Air, &V. when 
made very thin by being blown 
into Bubbles, or otherwife formed 
into Plates, do exhibit various Co- 
lours according to thcjr various thinnefs, altho' at 

a greater 




BOOK II. 169 

a greater tlucknefs they appear very clear and 
colour! efs. In the former Book I forbore to 
treat of, thefe Colours, becaufe they feemed of a 
more difficult Confideration, and were not necef- 
fary for eftabliihing the Properties of Light there 
difcourfed of. But becaufe they may conduce to 
farther Difcpveries for compleating the Theory of 
Light, efpecially as to the conftitution of the 
parts of natural Bodies, on which their Colours 
or Tranfparency depend j I have here fet down 
an account of thern. To render this Difcourfe 
fhort and didindt, I have fiifl defcribed the prin- 
cipal of my Obfervations , and then confider'd 
and made ufe of them. The Obfervations are 
thefe. 

Ohf. I., Comprefiing two Prifms hard toge- 
ther that their fides (which by chance were a 
very little convex) might fomewhere touch one 
another : I found the place in which they touch- 
ed to become abfolutely tranfparent, as if they 
had there been one continued piece of Glafs, 
For when the Light fell fo obliquely on the 
Air, which in other places was between them, 
as to be all refledcds ic feemed in that place of 
contact to be wholly tranfmitted, infomuch that 
when look'd upon, it appeared like a black or 
dark fpot, by reafon that little or no fenfible 
Light was refledled from thence, as from other 
places ; and when looked through it feemed ( a^ 
it were) a hole in that- Air which was formed 
into a thin Plate, by being comprefs'd between 
the Glafles. And through this hole Objeds that 
were beyond might be feen diftindly , which 
could not at all be feen through other parts of 

the 



lyo O P T I C K S. 

the GlafTes where -the Air was interjacent. Al- 
though the GlafTes were a little convex, yet this 
transparent fpot was of a confiderable breadth, 
which breadth feemed principally to proceed 
from the yielding inwards of the parts of the 
GlafTes, by reafon of their mutual prefTure. For 
by prefTing them very hard together it would be- 
come much broader than otherwife. 

Obf. 2. When the Plate of Air, by turning 
the Prifms about their common Axis, became (o 
little inclined to the incident Rays, that fome of 
them began to be tranfmitted, there arofe in it 
many flender Arcs of Colours which at firfl were 
fhaped almofl like the Conchoid , as you fee 
them delineated in the firfl Figure. And by con- 
tinuing the Motion of the Prifms, thefe Arcs 
increafed and bended more and more about the 
faid tranfparent fpot, till they were compleated 
into Circles or Rings incompafling it, and af- 
terwards continually grew more and more con- 
tradted. 

Thefe Arcs at their firfl appearance were of 
a violet and blue Colour, and between them 
were white Arcs of Circles , which prefently 
by continuing the Motion of the Prifms became 
a little tinged m their inward Limbs with red 
and yellow, and to their outward Limbs the 
blue was adjacent. So that the order of thefe 
Colours from the central dark fpot, was at that 
time white, blue, violet j black, red, orange, 
yellow, white, blue, violet, &c. But the yel- 
low and red were much fainter than the blue and 
violet. * 

2 ' The 



BOOK 11. 171 

The Motion of the Prifms aBout their Axis 
being continued, thefe Colours contracl^ed more 
and more, Shrinking towards the whitenefs on 
either fide of it, until they totally vaniihed into 
it. And then the Circles in thofe parts appear'd 
black and white, without any other Colours in~ 
termix'd. But by farther moving the Prifms 
about, the Colours again emerged out of the 
whitenefs, the violet and blue at its inward 
Limb, and at its outward Limb the red and yel- 
low. So that now their order from the central 
Spot was white, yellow, red; black; violet, 
.blue, white, yellow, red, ^c, contrary to what 
it was before. 

Obf. 3. When the Rings or fome parts of 
them appeared only black and white, they were 
very diftindl and well defined, and the blacknefs 
feemed as intenfe as that of the central Spot. 
Alfo in the Borders of the "Rings, where the 
Colours began to emerge out of the white- 
nefs, they were pretty diftind: , which made 
them vifible to a very great multitude. I have 
fometimes number'd above thirty Succeffions 
(reckoning every black and white Ring for one 
Succeflion) and feen more of them, which by 
reafon of their fmalnefs I could not number. 
But in other Pofitions of the Prifms, at which 
the Rings appeared of many Colours, I could 
not diftinguiih above eight or nine of them, and 
the Exterior of thofe were very confufed and 
dilute. 

In thefe two Obfervations to fee the Rings di- 
ilin<5t, and without any other Colour than bl^ck 
and white, I found it neceflary to hold my Eye 

at 



172 O P T I C K S. 

at a good diftance from them. For by ap- 
proachijfjg nearer, although in the fame inclina- 
tion of my Eye to the Plane of the Rings, there 
emerged a bluifH Colour out of the white, 
which by dilating it felf more and more into 
the black, render'd the Circles lefs diflindt, and 
left the white a little tinged with red and yel- 
low. I found alfo by looking through a flit or 
oblong hole, which was narrower than the pupil 
of my Eye, and held clofe to it pjirallel to the 
Piifms, I could fee the Circles much diftindter 
and vifible to a far greater number than other- 
wife. 

Ohf.\> To obferve more nicely the order of 
the Colours which arofe out of the white Cir- 
cles as the Rays became lefs and lefs inclined 
to the Plate of Airj I took two Objed-glafTes, 
the one a Plano-convex for a fourteen Foot 
Telefcope, and the other a large double Con- 
vex for one of about fifty Footj and upon this, 
laying the other with its plane fide downwards, 
I prelfed them (lowly together,, to make the 
Colours fucceffively emerge in the middle of the 
Circles, and then fiowly lifted the upper Glafs 
from the lower to make them fuccefTively vaniih 
again in the fame place. The Colour, which 
by preffing the GlalTes together, emerged laft in 
the middle of the other Colours, would upon its 
firft appearance look like a Circle of a Colour 
almoft uniform from the circumference to the 
center, and by compreffing the GlaiTes ftill more, 
grow continually broader until a new Colour 
emerged in its center, afid thereby it becanie a 
Ring encompaihng ^hat new Colour. And by 

2 com- 



BOOK IL t73 

domprefiing the Gkfles ftill more, the diameter 
of this Ring would increafe, and the breadth of 
its Orbit or Perimeter decreafe until another new 
Colour emerged in the center of the laft: And 
fo on until a third, a fourth, a fifth, and other 
following new Colours fuccefiively emerged 
there, and became Rings encompalfmg the inner- 
moft Colour, the laft of which was the black 
Spot. And, on the contrary, by lifting up the 
upper Glafs from the lower, the diameter of the 
Rings would decreafe, and the breadth of their 
Orbit increafe, until their Colours reached fuc- 
cefiively to the center ; and then they being of a 
confiderable breadth, I could more eafily difcern 
and diftinguifti their Species than before. And 
by this means I obferv'd their Succeflion and 
Quantity to be as foUoweth. 

Next to the pellucid central Spot made by 
the contadl of the Glaffes fucceeded blue, white, 
yellow, and red. The blue was ib little in quan- 
tity, that I could not difcern it in the Circles 
made by the Prifms, nor could I well diftinguifti 
any violet in it, but the yellow and red were 
pretty copious, and feemed about as much in 
extent as the white, and four or five times more 
than the blue. The next Circuit in order of 
Colours immediately encompaffmg thefe were 
violet, blue, green, yellow, and red: and thefe 
were all of them copious and vivid, excepting 
the green, which was very little in quantity, and 
feemed much more faint and dilute than the 
other Colours. Of the other four, the vio- 
let was the leaft in extent, and the blue lefs 
than the yellow or red. The third Circuit or 

^ Order 



174. O P T I C K S. 

Order was purple, blue, green, yellow, and 
red ; in which the purple feemed more reddifh 
than the violet in the former Circuit, and the 
green was much more confpicuous , being as 
brisk and copious as any of the other Colours, 
except the yellow, but the red began to be a lit- 
tle faded, inclining very much to purple. Af- 
ter this fucceeded the fourth Circuit of green 
and red. The green was very copious and live- 
ly, inclining on the one lide to blue, and on 
the othtr fide to yellow. But in this fourth 
Circuit there was neither violet, blue, nor yel- 
low, and the red was very imperfe6l and dir- 
ty. Alfo the fucceeding Colours became more 
and more imperfed: and dilute, till after three 
or four revolutions they ended in perfedt 
whitenefs. Their form, when the Glafles were 
moft comprefs'd fo as to make the black Spot 
appear in the center, is delineated in the fe- 
Gond Figure ; where a, b, f, ^, e : /, ^, h, /, 
k : /, w, w, 0, p: q, r : s, t : v, x : )\ z, de- 
note the Colours reckon'd in order from the 
center, black, blue, white, yellOw, red: vio- 
let, blue, green, yellow, red: purple, blue, 
green, yellow, red: green, red: greenifh blue, 
red: greenifli blue, pale red: greenifli blue, 
reddifh white. 

Obf. 5. To determine the interval of the 
Glalfes, or thicknefs of the interjacent Air, by 
which each Colour was produced, I meafured 
the Diameters of the firfl fix Rings at the moft 
lucid part of their Orbits, and fquaring them, I 
found their Squares to be in the arithmetical Pro- 
greffion of the odd Numbers, i, 3, 5, 7, 9, 1 1. 

And 



BOOK II. 175 

And fince one of thefe Glafles was plane, and 
the other fpherical, their Intervals at thofe Rings 
jnuft be in the fame Progreffion. I meafured alio 
the Diameters of the dark or faint Rings between 
the more lucid Colours, and found their Squares 
to be in the arithmetical Progrelfion of the. even 
Numbers, 2, 4, 6, 8, 10, 12. And it being very 
nice and difficult to take thefe meafures exadly; 
I repeated them divers times at divers parts of 
ihe GlafTes, that by their Agreement I might be 
confirmed in them. And the lame method I ufed 
in determining fome others of the following Ob- 
fervations. 

Obf. 6. The Diameter of the fixth Ring at 

the moil lucid part of its Orbit was -^ parts of 

an Inch, and the Diameter of the ' Sphere on 
which the double convex Objedt-glals was 
ground was about 102 Feet, and hence I ga- 
thered the thicknefs of the Air or Aereal Inter- 
val of the Glaffes at that Ring. But fome time 
after, fufpedting that in making this Obfervatioii 
I had not determined the Diameter of the 
Sphere with fufficient accuratenefs, and being 
uncertain whether the Plano-convex Glafs was 
truly plane, and not fomething concave or con- 
vex on that fide which I accounted plane ; and 
whether I had not preiTed the GlafiTes together, 
as I often did, to make them touch j ( For by 
preffing fuch GlalTes together their parts eafily 
yield inwards, and the Rings thereby become 
fenfibly broader than they would be, did the 
GlalTes keep their Figures.) I repeated the 
Experiment , and found the Diameter of the 

fixth 



176 O P T I C K S. 

fixth Iticid Ring about -^ parts of an Inch. 1 

repeated the Experiment alfo with fuch an Ob- 
jed-glafs of another Tclefcope as I had at hand. 
This was a double Convex ground on both 
fides to one and the fame Sphere, and its Fo- 
cus was diftant from it 83 f Inches. And thence, 
if the Sines of Incidence and Refraction of the 
bright yellow Light be affumed in proportion 
as II to 17, the Diameter of the Sphere to 
which the Glafs was figured will by computa- 
tion be fougd 182 Inches. This Glafs I laid 
upon a flat one, fo that the black Spot appear- 
ed in the middle of the Rings of Colours with- 
out any other PrelTure than that of the weight 
of the Glafs. And now meafuring the Diame- 
ter of the fifth dark Circle as accurately as I 
could, I found it the fifth part of an Inch pre- 
cifely. This Meafure was taken with the point$ 
of a pair of CompaiTes on the upper Surface 
on the upper Glafs, and my Eye was about 
eight or nine Inches diftance from the Qlafs, 
almofl perpendicularly over it, 'and the Glafs 
was r of an Inch thick, and thence it is eafy to 
colled: that the true Diameter of the Ring be- 
tween the Glaffes was greater than its meafur'd 
Diameter above the Glaffes in the Proportiort 
of 80 to y9, or thereabouts, and by confequence 
equal to ^| parts of an Inch, and its true Semi- 
diameter equal to tV parts. Now as the Dia- 
meter of the Sphere (.182 Inches) is to the Se- 
mi-diameter of this fifth dark Ring .(t* parts of 
an Inch) fo is this Semi-diameter to the thick- 
: nefs of the Air at this fifth dark Ring j which is 

there- 



BOOK II. ?t77 

therefore -7^^— or — ^^ Parts of an Inch ; and 
^ 567931 1774784 ^ 

the fifth Part thereof, viz. tke -r^ Part of an 

•0739 

Inch, is the Thicknefs of the Air at thefirft 
of thefe dark Rings. 

The fame Experiment I repeated with another 
double convex Objed'-glafs ground on both fides 
to one and the fame Sphere. Its Focus was di- 
flarit from it i68j Inches, and therefore the Dia- 
meter of that Sphere was iS'4 Inches. This 
Glafs being laid upon the fijme plain, Glafs, 
the Diameter of the fifth of the dark Rings, 
when the black Spot in their Center appear'd 
plainly without preffing the Glailes, was by the 
meafure of the Compafles upon fhe upper Glafs 

!ii Parts of an Inch, and by. confequence be- 
tween theGlaffes it was ~^:.. For the upper Glafs 

was ^ of an Inch thick, arid rhy Eye was diitant 
from it 8 Inches. And a third proportional to 
"half this from the Diameter ,,©jf the/Sphere is 

,,-r- Parts of an Inch. Thi^ is therefore the 
Thicknefs of the Air at this. Ring, and a fifth 
Part thereof, viz. the ~— th Part of. an Incli is 

the Thicknefs thereof at the firfl of the Rings, as 
above. 

I tried the fame Thing, by laying thefe Obje(5t- 
glafies upon flat Pieces of a broken Looking- 
glafs, and found the fame Meafures of the 
Rings: Which makes me rely upon them till 

N they 



178 O P T I C K S. 

.they can be determin'd more accurately byGlailes 
ground to larger Spheres, though in fuch GlafTes 
greater care muft be taken of a true Plane. 

Thefe Dimenfions were taken, when my Eye 
was placed almoft perpendicularly over the Glaf- 
fes, being about an Inch, or an Inch and a quar- 
ter, diilant from the incident Rays, and eight 
Inches diftant from the Glafs j fo that the Rays 
were inclined to the Glafs in an Angle of about 
four Degrees. Whence by the following Obfer- 
vation you will underftand, that had the Rays 
been perpendicular to the GlafTes, the Thicknefs 
of the Air at thefe Rings would have been lefs ia 
the Proportion of the Radius to the Secant of four 
Degrees, that is, of loooo to 10024. Let the 
ThicknefTes found be therefore dimini{h'd in this 

Proportion, and they will become —^ and --^ — ^. 

or ( to ufe the nearefl round Number ) the 

g~^th Part of an Inch. This is the Thicknefs of 

the Air at the darkeft Part of the iirft dark Ring 
made by perpendicular Rays; and half this Thick- 
nefs multiplied by the ProgreiTion,' i, 3, 5, 7, g^ 
iiy^^c. gives the Thicknefles of the Air at the 
moft luminous Parts of all the brighteft Rings, viz, 

{^y T^o) T^oy r78^> ^^' ^heir arithme- 
tical Means ^^, - g^~, ^j^^, &c. being its 
ThicknefTes at the darkefl Parts of all the dark 
ones. 



Oi/.j. 



BOOK IL 



179 



Obf. 7. The Rings were leaft, when my Eye 
was placed perpendicularly over theGlafTes in the 
Axis of the Rings : And when I view'd them 
obliquely they became bigger, continually fwel- 
ling as I removed my Eye farther from the Axis. 
And partly by meafuring the Diameter of the 
fame Circle at feveral Obliquities of my Eye, 
partly by other Means, as alfo by making ufe of 
the two Prifms for very great Obliquities, I found 
its Diameter, and confequently the Thicknefs of 
the Air at its Perimeter in all thofe Obliquities to 
be very nearly in the Proportions exprefs'd in 
this Table. 



Angle of In- 


Angle of Re- 


Diameter 


"Ihickricf 


cidence on 


f ration in- 


of the 


of the 


the Air. 


to the Air. 


Ring. 


Air. . 


Deg. Min. 








00 00 


00 00 


10 


\^ 


06 26 


10 00 


IOtV 


IOtV 


12 45 


20 00 


lOf 


IQi 


18 49 


30 00 


lOA 


Ilf 


24 30 


40 00 


IIv 


13 


29 37 


50 00 


12k 


i5i 


33 58 


60 00 


14 


20 


35 47 


65 00 


i5i 


23t 


37 19 


70 00 


i6t 


28^ 


3S 33 


7S 00 


'^I 


37 


39 27 


'80 00 


22f 


52i 


40 00 
.. 40 II 


85 GO 


29 


Hu 


90 00 


3< 


\ 122', 



N 2 



In 



i8o O P T I C K S. 

* In the two firll Columns are exprefs'd the Obli- 
quities of the incident and emergent Rays to the 
Plate of the Air, that is, their Angles of Inci- 
dence and Refraction. In the third Column the 
Diameter of any colour'd Ring at thofe Obliqui- 
ties is exprelTed in Parts, of which ten conffcitute 
that Diameter when the Rays are perpendicular. 
And in the fourth Column the Thicknefs of 
the Air at the Circumference of that Ring is 
exprelTed in Parts, of which alfo ten eonfti- 
tute its Thicknefs when the Rays are perpen- 
dicular. 

And from thefe Meafures I feem to gather 
this Rule: That the Thicknefs of the Air is pro- 
portional to the Secant of an Angle, whofe Sine* 
is a certain mean Proportional between the Sines.' 
of Incidence and Refradlion. Arid that mean 
. Proportional, fb far as by thefe Meaftires I caw 
determine it, is the firft of an hundred and fix 
arithmetical mean Proportionals between thofe» 
Sines counted from the bigger Sine, that; is, 
* from the Sine of Refradion when the Re- 
fraction is made out of the Glafs into the^ 
Plate of Air, or from the Sine of Incidence when* 
the Refraftion is made out oi the ■ Plate of Air 
into the Glafs. , 

O^.' 8. The dark Spot in the middle of the 
Rings increafed alfo by the Obliquation of the 
Eye, although almofl infenfibly. But, if inftead 
of the ObjeS-glafTes the Prifms were made ufe 
of, its Increafe was more manifefl when viewed 
fo, obliquely that no Colours appeared about 
it. ' It was leafl when the Rays were incident 
moll obliquely on the interjacent Air, and as 

the 



BOOK II. i8i 

the obliquity decreafed it increafed more and 
more until the colour'd Rings appear'd, and 
then decreafed again, but not fo much as it in- 
creafed before. And hence it is evident, that 
the Tranfparency was not only at the abfolute 
Contad of the GlalTes, but alfo^here they had 
fome little Interval. I have fometimes obferved 
the Diameter of that Spot to be between half 
and two fifth parts of the Diameter of the ex- 
terior Circumference of the red in the firft Cir- 
cuit or Revolution of Colours when view'd al- 
moft perpendicularly ; whereas when view'd ob- 
liquely it hath wholly vanifli'd and become 
opake and -white like the other parts of the 
Glafs 3 whence it may be coUeded that the 
Glaffes did then fcarcely, or not at all, touch 
one another, and that their Interval at the pe- 
rimeter of that Spot when view'd perpendicu- 
larly was about a fifth or fixth part of their In- 
terval at the circumference of the faid red. 

O/y^rT'. 9.. By looking through the two conti- 
guous Objed-glafies, I found that the interja- 
cent Air exhibited Rings of Colours, as well 
by tranfmitting Light as by refleding it. The 
central Spot was now white, and from it the 
order of the Colours were yellowifli red; black, 
violet, blue, white, yellow, red; violet, blue, 
green, yellow, red, &c. But thefe Colours 
were very faint and dilute, unlefs when the 
Light was trajecled very obliquely through the 
Glaffes : For by that means they became pretty 
vivid. Only the firft yellowifh red , like the 
blue in the fourth Obfervation, was fo little and 
faint as fcarcely to be difcern'd. Comparing 

N 3 the 



i82 O P T I C K S. 

the colour'd Rings made by Reflexion, with 
thefe made by tranfmilTion of the Light j I 
found that white was oppofite to black, red to 
blue, yellow to violet, and green to a Compound 
of red and violet. That is, thafe parts of the 
Glafs were black when looked through, which 
when looked upon appeared white, and on the 
contrary. And fo thofe which in one cafe exhi- 
bited blue, did in the other cafe exhibit red. 
And the like of the other Colours. The man- 
ner you have reprefented in the third Figure, 
where A B, CD, are the Surfaces of theGlaifes 
contiguous at E, and the black Lines between 
them are their Diftances in arithmetical Progref-. 
iion, and the Colours written above are feen by 
refiedied Light, and thofe below by Light tranf- 
mitted. 

Oof. 10. Wetting the Objed-glafTes a little 

■ at their edges, the Water crept in flowly be- 
tween them, and the Circles thereby became 
lefs and the Colours more faint : Infomuch that 
as the Water crept along, one half of them at 
which it firft arrived would appear broken off 
from the other half, and contracted into a lefs 
Room. By meafuring them I found the Pro- 
portions of their Diameters to the Diameters of 
the like Circles made by Air to be about itvtu. 
to eight, and confequently the Intervals of the 
Glaffes at like Circles, caufed by thofe two Me- 
diums Water and Air, are as about three to four. 

• Perhaps it may be a general Rule, That if any 
other Medium more or lefs denfe than Water 
be comprefs'd between the Glaffes, their Inter- 
vals at the Rings cavifed thereby will be to their 

Intervals 



BOOK II. 183 

Intervals caufed by interjacent Air, as the Sines 
are which meafure the Refrad;ion made out of 
that Medium into Air. 

Obf. II. When the Water was between the 
Glafles, if I prefTed the upper Glafs varioully at 
its edges to make the Rings move nimbly from 
one place to another, a little white Spot would 
immediately follow the center of them, which 
upon creeping in of the ambient Water into that 
place would prefently vanilh. Its appearance 
was fuch as interjacent Air would have caufed, 
and it exhibited the fame Colours. But it was 
not Air, for where any Bubbles of Air were in 
the Water they would not vanilli. The Refle- 
xion- muft have rather been caufed by a fubtiler 
Medium, which could recede through the Glaf-^ 
fes at the creeping in of the Water. 

Obf. 12. Thefe Obfervations were made in 
the open Air. But farther to examine the Effects 
of colour'd Light falling on the Glaffes, I dar- 
3cen'd the Room, and view'd them by Reflexion 
of the Colours of a Prifm caft on a Sheet of 
white Paper, my Eye being fo placed that I 
could fee the colour'd Paper by Reflexion in the 
Glalfes , as in a Looking-glals. And by this 
means the Rings became diftind:er and vifible to 
a far greater number than in the open Air. I 
have fometimes feen more than twenty of them, 
whereas in the open Air I could not difcern above 
eight or nine. 

Obf. 13. Appointing an A ffiftant to move the 
Prifm to and fro about its Axis, that ail the 
Colours might fucceffively fall on that part of 
the Paper which I faw by Reflexion from that 

N 4 part 



j84 OPTIC K S. 

part of "the GlafTes, where the Circles appear'd, 
£o thax all. the Colours might be fucceffively re, 
fiefted from the Circles to my Eye whilft I held 
it immovable, I found, the Circles which the 
red Light made to be manifeftly bigger than 
thofe which were made by the blue and violet. 
And it was very pleafant to fee them gradually 
fwell or contrad: accordingly as the Colour of the 
Light was changed. The Interval of the Glaf- 
fes at any of the Rings when they were made by 
|:he utmoft red Light, was to their Interval at the 
fame Ring when made by the utmoft violet, 
greater than as 3 to 2, and lefs than as 13 to 8. 
By the moft of my Obfer vat ions it was as 14 to 
9. And this Proportion feem'd very nearly the 
fame in all Obliquities of my Eye ; unlefs whea 
two Prifms were made ufe of inftead of the Ob^ 
jedi-glafTes. For then at a certain great obliquity 
of my Eye, the Rings made by the feveral Co- 
lours {eem'd equal, and at a greater obliquity 
thofe made by the violet would be greater than 
the fame Rings made by the red: the Refrad:ion 
of the Prifm in this cafe caafing the moft refran^ 
gible Rays to fall more obliquely on that plate of 
the Air than the leaft refrangible ones. Thus 
the Experiment fucceeded in the colour'd Light, 
which was fufhciently ftrong and copious to 
jnake the Rings fenfible. And thence it may be 
gather'd, that if the moft refrangible and leaft 
refrangible Rays had been copious enough to 
make the Rings fenfible without the mixture of 
other Rays, the Proportion which here was 14 to 
9 would have been a little greater, fuppofe 14? 
or 14T to 9. 



BOOK IT. 185 

Obf. 14. Whilft the Prifm was turn'd about 
its Axis with an uniform Motion, to make all 
the feveral Colours fall fucceffively upon the 
Objedi-glafles, and thereby to marke the Rings 
contrad: and dilate : The Contradion or Dilata- 
tion of each Ring thus made by the variation of 
its Colour was fwifteft in the red, and floweft 
in the violet, and in the intermediate Colours 
it had intermediate degrees of Celerity. Com- 
paring the quantity of Contrad:ion and Dilata- 
tion made by all the degrees of each Colour, I 
found that it was greatefl in the red j lefs in 
the yellow, ftill lefs in the blue, and leaft in the 
violet. And to make as juft an Eftimation as I 
could of the Proportions of their Contrad:ions 
or Dilatations, I obferv'd that the whole Con- 
traction or Dilatation of the Diameter of any 
Ring made by all the degrees of red, was to 
that of the Diameter of the fame Ring made by 
all the degrees of violet, as about four to three, 
or five to four, and that when the Light was 
of the middle Colour between yellow and green, 
the Diameter of the Ring was very nearly an 
arithmetical Mean between the greatefl Diame- 
ter of the fame Ring made by the outmoft red, 
and the leaft Diameter thereof made by the 
outmoft violet : Contrary to what happens in 
the Colours of the oblong Spedlrum made by 
the Refraction of a Prifm, where the red is 
moft contracted , the violet moft expanded , 
and in the midft of all the Colours is the Con- 
fine of green and blue. And hence I feem to 
collect that the thicknefies of the Air between 
the GlaiTcs there, where the Ring is fucceffive- 
ly 



i86 O P T I C K S. 

ly made by the limits of the five principal Co- 
lours ( red, yellow, green, blue, violet ) in or- 
der ( that is, by the extreme red, by the limit 
of red and yellow in the middle of the orange, 
by the limit of yellow and green, by the limit 
of green and blue, by the limit of blue and 
violet in the middle of the indigo, and by the 
extreme violet ) are to one another very nearly 
as the fixth lengths of -aXhord which found the 
Notes in a fixth Major, Jhl^ la, mi\ fa, Jol, la. 
But it agrees fomething better with the Obferva- 
tion to fay, that the thickneffes of the Air be- 
tween the GlafTes there, where the Rings are 
fuccefTively made by the limits of the feven Co- 
lours, red, orange, yellow, green, blue, indi- 
go, violet in order, are to one another as the 
Cube Roots of the Squares of the eight lengths 
^f a Chord, which found the Notes in an eighth, 
Jhl, la, fa, Jbl, la, mi, fa, fol ; that is, as the 
Cube Roots of -the Squares of the Nurinbers, i, 

8 f J i i ^ I 

§> 5> 4J 1; Si '^J 2* 

Obf 15. Thefe Rings were not of various 
Colours like thofe made in the open Air, but 
appeared all over of that prifmatick Colour on- 
ly witli which they were illuminated. And by 
projediing the prifmatick Colours immediately 
upon the GlalTes, I found that the Light which 
fell on the dark Spaces which were between 
the colour'd Rings was tranfmitted through the 
GlalTes without any variation of Colour. For 
on a white Paper placed behind, it would paint 
Rings of the fame Colour with thofe which 
were refleded, and of the bignefs of their im- 
mediate Spaces. And from thence the origin 

I of 



BOOK II. 187 

of thefe Rings Is manifefl; namely, that the Air 
.between the Glaffes, according to its various 
thicknefs, is difpofed in fome places to refledt, 
and in others to tranfmit the Light of any one 
Colour (as you may fee reprefented in the 
fourth Figure ) and in the fame place to refled: 
that of one Colour where it tranfmits that of 
another. , 

Obf. 16. The Squares of the Diameters of 
thefe Rings made by any prifmatick Colour were 
in arithmetical Progrefilon, as in the fifth Ob- 
fervation. And the Diameter of the fixth Cir- 
cle, when made by the citrine yellow, and 

viewed almofl perpendicularly, was about ^ 

parts of an Inch, or a little lefs, agreeable to the 
fixth Obfervation. 

The precedent Obfervations were made with 
a rarer thin Mediuni; terminated by a denfer, 
fuch as was Air or Water comprefs'd between 
two GlalTes. In thofe that follow are fet down 
the Appearances of a denfer Medium thin'd 
within a rarer, fuch as are Plates of Mufcovy 
Glafs, Bubbles of Water, and fome other thin 
Subftances terminated on all fides with Air. 

Obf. 17. If a Bubble be blown with Water 
firft made tenacious by dilTolving a little Soap 
in it, 'tis a common Obfervation, that after a 
while it will appear tinged with a great variety of 
Colours. To defend thefe Bubbles from being 
agitated by the external Air (whereby their Co- 
lours are irregularly moved one among ano- 
ther, fo that no accurate Obfervation can be 
made of themj as foon as I had blown any of 

thorn 



i88 OPTIC K S. 

them I cover'd it with a clear Glafs, and by that 
means its Colours emerged in a very regular 
order, like fo many concentrick Rings encom- 
paffing the top of the Bubble. And as the Bub- 
ble grew thinner by the continual fubfiding of 
the Water, thefe Rings dilated flowly and over- 
fpread the whole Bubble, defcending in order to 
the bottom of it, where they vanifn'd fuc- 
celTively. In the mean while, after all the Co- 
lours were emerged at the top, there grew in the 
center of the Rings a fmall round black Spot, 
like that in the firft Obfervation, which con- 
tinually dilated it felf till it became fometimes 
more than i or ^ of an Inch in breadth before 
the Bubble broke. At firft I thought there had 
been no Light refleded from the Water in that 
place, but obferving it more curioufly, I faw 
within it feveral fmaller round Spots, which 
appeared much blacker €nd darker than the 
reft, whereby I knew that there was fome Re- 
flexion at the other places which were not fo 
dark as thofe Spots. And by farther Tryal I 
found that I could fee the Images of fome 
things (as of a Candle or the Sun) very faintly 
refled:ed, not only from the great black Spot, 
but alfo from the little darker Spots which were 
within it. 

Belides the aforefaid colour'd Rings there 
would often appear fmall Spots of Colours, af- 
cending and defcending up and down the fides 
of the Bubble, by reafon of fome Inequalities in 
the fubfiding of the Water. And fometimes 
fmall black Spots generated at the fides would 
2 afcend 



BOOK II. 189 

afcend up to the larger black Spot at the top of 
the Bubble, and unite with it. 

ObJ. 18. Becaufe the Colours of thefe Bubbles 
were more extended and lively than thofe of the 
Air thinn'^d between two GlafTes, and fo more 
eafy to be diiliinguilli'd, I Ihall here give you a 
farther defcription of their order, as they were 
obferv'd in viewing them by Reflexion of the 
Skies when of a white Colour, whilft a black 
fubftance was placed behind the Bubble. And 
they were thele, red, blue; red, blue; red, 
blue; red, green; red, yellow, green, blue, 
purple; red, yellow, green, blue, violet; red, 
yellow, white, blue, black. 

The three fir ft Succeffions of red and blue 
were very dilute and dirty, efpecially the firft, 
where the red feem'd in a manner to be white. 
Among thefe there was fcarce any other Colour 
fenfible befides red an^ blue, only the blues ( and 
principally the fecond blue ) inclined a little to 



green. 



The fourth red was alfo dilute and dirtv, bur 
not fo much as the former three ; after that fuc- 
ceeded little or no yellow , but a copious 
green, which at firft inclined a little to yellow, 
and then became a pretty brisk and good wil- 
low green, and afterwards changed to a bluiib 
Colour; but there fucceeded neither blue noF 
violet. • 

The fifth red at firft inclined very much to 
purple, and afterwards became more bright 
and brisk, but yet not very pure. This was 
fucceeded with a very bright and intenfe yel- 
low» which was but little in quantity, and foon 

chang'd 



xgo O P T I C K S. 

chang'4 to green: But that green was copious 
and fomething more pure, deep and lively, than 
the former green. After that follow'd an ex- 
cellent blue of a bright Sky-colour, and then a 
purple, which was lefs in quantity than the blue, 
and much inclined to red. 

The fixth red was at firft of a very fair and 
lively fcarlet, and foon after of a brighter Co- 
lour, being very pure and brisk, and the beft 
of all the reds. Then after a lively orange fol- 
low'd an intenfe bright and copious yellow, 
which was alfo the beft of all the. yellows, and 
this changed firft to a greenifti yellow, and then 
to a greenifli bluej but the green between the 
yellow and the blue, was very little and dilute, 
feeming rather a greenifli white than a green. 
The blue which fucceeded became very good, 
and of a very fair bright Sky-colour, but yet 
fomething inferior to the former blue 3 and the 
violet was intenfe and deep with little or no 
rednefs in it. And lefs in quantity than the 
blue. 

In the laft red appeared a tin6lure of fcarlet 
next to violet, which foon changed to a bright- 
er Colour, inclining to an orange j and the yel- 
low which follow'd was at firft pretty good 
and lively, but afterwards it grew more dilute, 
until by degrees it ended in perfed: whitenefs. 
And this whitenefs, if the Water was very te- 
nacious and well-temper'd, would fiowly fpread 
and dilate it felf over the greater part of the 
Bubble; continually growing puler. at the top, 
where at length it would crack in many places, 
and thofe cracks, as they dilated, would appear 

of 



BOOK II. . rgt 

of a pretty good, but yet obfcure and dark 
Sky-colour; the white between the blue Spots 
diminifliing, until it refembled the Threds of 
an irregular Net-work, and foon after vanifh'd, 
and left all the upper part of the Bubble of the 
faid dark blue Colour. And this Colour, after 
the aforefaid manner, dilated it felf downwards, 
until fometimes it hath overfpread the whole 
Bubble. In the mean while at the top, which 
was of a darker blue than the bottom, and ap- 
pear'd alfo full of many round blue Spots, fome- 
thing darker than the reft, there woiild emerge 
one or more very black Spots, and within thofe, 
other Spots of an intenfer blacknefs, which I 
mention'd in the former Obfervation ; and thefe 
continually dilated themfelves until the Bubble 
broke. 

If the Water was not very tenacious, the black 
Spots would break forth in the white, without 
any fenfible intervention of the blue. And fome- 
times they would break forth within the prece- 
dent yellow, or red, or perhaps within the blue 
of the fecond order, before the intermediate Co- 
lours had time to difplay themfelves. 

By this defcription you may perceive how great 
an affinity thefe Colours have with thofe of Air 
defcribed in the fourth Obfervation, although 
fet down in a contrary order, by reafon that 
they begin to appear when the Bubble is thick- 
eft, and are moft conveniently reckon'd from 
the loweft and thickeft part of the Bubble up- 
wards. 

Obf. 19. Viewing in feveral oblique Poiitions 
of my Eye the Rings of Colours emerging on 

the 



192 O P T I C K S. 

the top of the Bubble, I found that they were 
fenfibly dilated by increafing the obliquity, but 
yet not fo much by far as thofe made by thinn'd 
Air in the feventh Obfervation. For there they 
v/ere dilated fo much as, when view'd moft ob- 
liquely, to arrive at a part of the Plate more than 
twelve times thicker than that where they ap- 
pear'd when viewed perpendicularly j whereas ii;i 
this cafe the thicknefs of the Water, at which 
they arrived when viewed moil obliquely, was to 
that thicknefs which exhibited them by per- 
pendicular Rays, fomething lefs than as 8 to 5'. 
By the beft of my Obfervations it was between 
15 and 15; to 10; an increafe about 24 times lefs 
than in the other cafe. 

Sometimes the Bubble would become of an 
uniform thicknefs all over, except at the top of 
it near the black Spot, as I knew, becaufe it 
would exhibit the fame appearance of Colours 
in all Portions of the Eye. And then the Co- 
lours which were feen at its apparent circumfe- 
rence by the obliquefl Rays, would be different 
from thofe that were feen in other places, by 
Rays lefs oblique to it. And divers Spedtators 
might fee the fame part of it of differing Co- 
lours, by viewing it at very differing Obliqui- 
ties. Now obferving how much the Colours at 
the fame places of the Bubble, or at divers pla* 
ces of equal thicknefs, were varied by the fe- 
veral Obliquities of the Rays; by the affiflance 
of the 4th, 14th, 1 6th and i8th Obfervations, 
as they are hereafter explain'd, I colled: the 
thicknefs of the Water requifite to exhibit any 
one and the fame Colour, at feveral Obliquities, 

to 



BOOK II. 



193 



to be very nearly in the Proportion expTeffed in 



this Table. 



Incidence on 
the Water. 


Rejra5lion into 
the Water. 


Thicknefs of 
the Water. 


Deg. Min. 


Deg. Min. 




00 00 


00 00 


10 


15 00 


II II 


loi 


30 00 


22 I 


10^ 


45 00 
60 00 

7S 00 
90 00 


32 2 

40 30 

• 46 25 

48 35 


I If 
13 



In the two firft Columns are exprefs'd the 
Obliquities of the Rays to the Superficies of the 
Water, that is, their Angles of Incidence and 
Refradion. Where I fuppofe^ that the Sines 
which meafure them are in round Numbers, as 
3 to 4, though probably the DifTolution of Soap 
in the Water, may a little alter its refradive 
Virtue. In the third Colpmn, the Thicknefs of 
the Bubble, at which any one Colour is exhibit- 
ed in thofe feveral Obliquities, is exprefs'd in 
Parts, of which ten conftitute its Thicknefs when 
the Rays are perpendicular. And the Rule 
found by the feventh Obfervation agrees well 
with thefe Meafures, if duly apply'd -, namely, 
that the Thicknefs of a Plate of Water requifite 
to exhibit one and the fame Colour at feveral 
Obliquities of the Eye, is proportional to the 
Secant of an Angle, whofe Sine is the firft of an 
hundred and fix arithmetical mean. Proportion 

O. nals 



194 OP TIC KS. 

nals between the Sines of Incidence and Refradion ^ 
counted from the lelTer Sine, that is, from the 
Sine of Refrad:ion when the Refradion is made 
out of Air into Water, otherwife from the Sine 
of Incidence. 

I ,have fometimes obferv'd, that the Colours 
whi<;h arife on polifh'd Steel by heating it, or on 
Bell-metal, and fome other metalline Sub- 
ftances, when melted and pour'd on the Ground, 
where they may cool in the open Air, have, like 
the Colours of Water-bubbles, been a little 
changed by viewing them at divers Obliquities, 
and particularly that a deep' blue, or violet, 
when view'd very obliquely, hath been changed 
to a deep red. But the Changes of thefe Co- 
lours are not fo great and fenfible as of thofe 
made by Water. For the Scoria, or vitrified Part 
of the Metal, which mofl Metals when heated or 
melted do continually protrude, and fend out 
to their Surface, and which by covering the 
Metals in form of a thin glafly Skin, caufes 
thefe Colours, is much denfer than Water ; and 
I find that the Change made by the Obliquation 
x)f the Eye is leaft in Colours of the denfeft thin 
Subilances. 

Obf. 20. As in the ninth Obfervation, fo here, 
the Bubble, by tranfmitted Light, appear'd of a 
contrary Colour to that which it exhibited by 
Reflexion. Thus when the Bubble being look'd 
on by the Light of the Clouds reflected from 
it, feemed red at its apparent Circumference, 
if the Clouds at the fame time, or immediately 
after, were view'd through it, the Colour at its 
Circumference would be blue-. And, on the 

contrary. 



BOOK IL 19$ 

.contrary, when by refleded Light it appeared 
blue, it would appear red by tranfmitted Light. 

Obf. 2 1. By wetting very thin Plates of Muf- 
CGvy Glals, whole thmnels made the like Co- 
lours appear, the Colours became more taint and 
languid , efpecially by wetting the Plates on 
that fide oppofite to the Eye: But I could not 
perceive any variation of their Species. So then 
the thicknefs of a Plate requiiite to produce 
any Colour, depends only on the denlity of the 
Plate, and not on that of the ambient Medium. 
And hence, by the loth and i6th Obfervations, 
may be known the thicknefs which Bubbles of 
Water, or Plates of Mufco'-cy Glafs, or other 
Subftances, have at any Colour produced by 
them. 

Obf, 22. A thin tranfparent Body, which is 
denfer than its ambient Medium, exhibits more 
brisk and vivid Colours than that which is fo 
much rarer; as I have particularly obferved iii 
the Air and Clafs. For blowing Glafs very thin 
at a Lamp Furnace, thofe Plates encompalTed 
with_ Air did exhibit Colours much more vivid 
than thofe of Air made thin between two Glaf- 
fes. 

Obf. 23. Comparing the quantity of Light 
refledted from the feveral Rings, I found that 
it was mpft copious from the iiril or inniofi;, 
and in the exterior Rings became gradually lef^ 
and lefs. Alfo the whitenefs of the iirft Ring 
was flronger than that refleded from thofe 
parts of the thin Medium or Plate which wxre 
without the Rings j as I co aid manifeftly per- 
ceive by viewing at a diftance the Rings made 

C a by 



196 O P T I C K S. 

by the two Objed-glafTes ; or by comparing tw6 
Bubbles of Water blown at diflant Times, in the 
firft of which the Whitenefsappear'd, which fuc- 
ceeded all the Colours, and in the other, the 
Whitenefs which preceded them all. 

Obf. 24. When the two Objeil-glafTes were 
lay'd upon one an cither, fo as to make the Rings- 
of the Colours appear, though with my naked Eye 
I could not difcern aljove eiffht or nine of thofe 

o 

Rings, yet by viewing them through a Prifm I 
have feen a far greater Multitude, infomuch that 
I could number more than forty, befides many 
others, that were fo very fmall and clofe together, 
that I could not keep my Eye fteady on them fe- 
verally fo as to number them, but by their 
Extent I have fometimes eftimated them to be 
more than an hundred. And I believe the Expe- 
riment may be improved to the Difcovery of far 
greater Numbers. For they feem to be really un- 
limited, though vifible only fo far as they can be 
feparated by the Refradion of the Prifm, as I (hall 
hereafter explain. 

But it was but one fide of thefe Rings, namely, 
that towards which the Refraction was made, 
which by that Refradion was render'd diftind:, 
and the other fide became more confufed than 
when view'd by the naked Eye, infomuch that 
there I could not difcern above one or two, 
and fometimes none of thofe Rings, of which 
I could difcern eight or nine with my naked 
Eye. And their Segments or Arcs, which on 
the other fide appear'd fo numerous, for the 
moft part exceeded not the third Part of a Cir- 
cle. If the Refraction was very great, or the 

Prifm 



B O O K II. 197 

Prilm very diftant from the Ohjed-glalTes, the 
middle Part of thofe Arcs became alfo confu- 
fed, fo as to difappear and conftitute an even 
Whitenefs, whiUl on either fide their Ends, as 
alfo the whole Arcs farthefl from the Center, 
became diftinder than before, appearing in the 
Form as you fee them defign'd in the hfth Fi- 
gure. 

The Arcs, where they feem'd diflindteft, were 
only white and black fuccellively, without any 
other Colours intermix'd. But in other Places 
there appeared Colpurs, whofe Order was inverted 
by the Kefradtion in fuch manner, that if I firft 
held the Prifm very near the Objedt-glafles, and 
then gradually removed it farther off towards my 
Eye, the Colours of the 2d, 3d, 4th, and fol- 
lowing Rings flirunk towards the white that 
emerged between them, until they wholly va- 
nifli'd into it at the middle of the Arcs, and 
afterwards emerged again in a contrary Order. 
But at the Ends of the Arcs they retain'd their 
Order unchanged. 

I have fometimes fo lay'd one Objed-glafs 
upon the other, that to the naked Eye they 
have all over feem'd uniformly white, without 
the leaft Appearance of any of the colour'd 
Rings ; and yet by viewing them through a 
Prifm, great Multitudes of thofe Rings have 
difcover'd themfelves. And in like manner 
Plates of Miifcovy Glafs, and Bubbles of Glafs 
blown at a Lamp-Furnace, which were not fo 
tlijn as to exhibit any Colours to the naked Eye, 
have through the Prifm exhibited a great Va^ 
riety of them ranged irregularly up and down in 

O 3 the 



198 O P T I C K S. 

the Form of Waves. And fo Bubbles of Water, 
before they began to exhibit their Colours to the 
naked Eye of aBy-ftander, have appeared through 
fl Prlfrn, girded about with many parallel and 
horizontal Rings ^ to produce v^hich Effed:, it 
was neceffary to hpld the Prifm parallel, or 
very nearly parallel to the Horizon, and to 
difpofe it {q th^t the Rays might be refraded 
upwards. 




T H»E 




THE 



SECOND BOOJ^ 



O F 



OPTICKS 



PART II. 



Remarks tipo-n the foregoing Obfervatio?ts, 

A V I N G given my Obfervations 
of thefe Colours, before I make 
life of them to unfold the Caufes 
of the Colours of natural Bodies, 
it is convenient that by the fim- 
pleft of them,fuch asare the ad, 3d, 
4th, 9th, I2thj 1 8th, 20th, and 24th, I firft ex- 

O 4 plaiu 




20O ; O P T I C K S. 

plain the more compounded. And firft to fhew 
now the Colours in the fourth and eighteenth 
Obiervations are produced, let there be taken in 
any Right Line from the Point Y, [in Ffg.6.] the 
Lengths YA, YB, YC, YD, YE, YF, YG, YH, 
in proportion to one another, as the Cube-RoOts 
of the Squares of the Numbers, 5, f^g, t, |, ^, |, |, i, 
whereby the Lengths of aMulical Chord to found 
all the Notes in an eighth are reprefented; that 
is, in the Proportion of the Numbers 6300, 68 14, 
71 14, 7631, 8255, 8855, 9243> loooo. And 
at the Points A, B, C, D, E, F, G, H, let Perpen- 
diculars A a, B /3, &c, be erefted, by whofe In- 
tervals the Extent of the feveral Colours fet under- 
neath againft them, is to be reprefented. Then 
divide the Line A a in fuch Proportion as the 
lumbers i, 2, 3, 5, 6, 7, 9, xo, 1 1, &c. fet at 
the Points of Divifion denote. And through 
thofe Divifions from Y draw Lines 1 1, 2 K, 3 L, 
5 M, 6 N, 7 O, &c. 

Now, if A 2 be fuppofed to reprefent the 
Thicknefs of any thin tranfparent Body, at which 
the outmoft Violet is moft copioully reflected 
in the firft Ring, or Series of Colours, then by 
the 13th Obfervation, HK will reprefent its 
Thicknefs, at which the utmoft Red is moft co- 
pioufly refleded in the fame Series. Alfo by 
the 5th and i6th Obfervations, A 6 and HN 
will denote the ThicknelTes at which thofe ex- 
treme Colours are moft copioufly refledied in 
the fecond Series, and A 10 and HQ^he Thick- 
neffes at which they are moft copioufly refledl- 
ed in the third Series, ■ and fo on. And the 
Thicknefs at which any of the intermediate Co- 
i lours 



BOOK II. 20I 

iours are reflefted moft copioufly, will, accor- 
ding to the 14th Obfervation, be defined by the 
diftance of the Line AH from the intermediate 
parts of the Lines 2 K, 6N, 10 Q, &c. againft 
which the Names of thofe Colours are written 
below. 

But farther, to define the Latitude of thefe 
Colours in each Ring or Series, let A i defign 
the leajft thicknels, and A 3 the greateft thi,ck- 
nefs , at which the extreme violet in the firft 
Series is reiledted, and let HI, and H L, de- 
fign the like limits for the extreme red, and let 
the intermediate Colours be limited by the in- 
termediate parts of the Lines il, and 3L, a- 
gainfi; which the Names of thofe Colours are 
written, and fo on: But yet with this caution, 
that the Reflexions be fuppofed flrongefl at the 
intermediate Spaces, 2K, 6N, ioQ> ci?r. and 
from thence to decreafe gradually towards thefe 
limits, 1 1, 3L, 5M, 7O, &c. on either fide; 
where you muft not conceive them to be pre- 
cifely limited, but to decay indefinitely. And 
whereas I have afiign'd the fame Latitude to e- 
very Series, I did it, becaufe although the Co- 
lours in the firfl Series feem to be a little broad- 
er than die* reft, by reafon of a ftronger Re- 
flexion tliere, yet that inequality is fo infenfi- 
ble as fcarcely to be determin'd by Obferva- 
tion. 

Now according to this Defcription, concei- 
ving that the Rays originally of feveral Colours 
are by turns refleded at the Spaces 1 1 L 3, 5M 
O7, 9P R 1 1, ^c. and tranfmitted at the Spaces 
AHIi, 3LM5, 7 OP 9, &c, it is eafy to know 

wliat 



202 O P T I C K S. 

what Colour muft in the open Air be exhi- 
bited at any thickneis of a tranlparent thin Bo- 
dy. For if a Ruler be -applied parallel to AH, 
at that diftance from it by which the thicknefs 
of the Body is reprefented, the alternate Spaces 
il L3, 5M O7, &c. which it croiTeth will de- 
note the reflected original Colours, of which 
the Colour exhibited in the open Air is com- 
pounded. Thus if the conftitutiop of the green 
in the third Series of Colours be defired, apply 
the Ruler as you fee at tt p cr 9, and by its paffing 
through fome of the blue at tt and yellow at cr, 
as' well as through the green at ^, you may con- 
clude that the green exhibited at that thicknefs of 
the Body is principally conflituted of original 
green, but not without a mixture of fome blue 
and yellow. 

By this means you may know how the Co- 
lours from the Center of the Rings outward 
ought to fucceed in order as they were defcri- 
bed in the 4th and i8th Obfervations. For if 
you move the Ruler gradually from AH through 
all diflances, having pafs'd over the firfl Space 
which denotes little or no Reflexion to be made 
by thinneft Subftances, it will firft arrive at i the 
violet, and then very quickly at the blue and 
green', which together with that violet com- 
pound blue, and then at the yellow and red, by 
whofe farther addition that blue is converted 
into whitenefs, which whitenefs continues du- 
ring the tranfit of the edge of the Ruler from 
I to 3, and after that by the fucceffive dehci- 
cnce of its component Colours, turns firfl to 
co-mpound yellow, and then to red, and lafl of 
9 all 



BOOK IT. 203 

■all the red ceafeth at L. Then begin the Co- 
lours of the fecond Series, which fucceed in 
order during the tranfit of the edge of the 
Ruler from 5 to O, and are more lively than 
before , becaufe more expanded and fevered. 
-And for the fame reafon, inftead of the former 
v^hite there intercedes between the blue and 
yellow a mixture of orange, yellow, green, 
blue and indigo, all which together ought to 
exhibit a dilute and imperfect green. So the 
Colours of the third Series all fucceed in or- 
der; firft, the violet, which a little interferes 
with the red of the fecond order, and is there- 
by inclined to a reddifli purple; then the blue 
and green, which are lefs mix'd with other 
Colours, and confequently more lively than be- 
fore, efpecially the green: Then follows the 
yellow, forne of which towards the green is di- 
Itintt and good, but that part of it towards the 
fucceeding red, as alfo that red is mix'd with 
the violet and blue of the fourth Series, where- 
by various degrees of red very much inclining 
to purple are compounded. This violet and 
blue, which fliould fucceed this red, being mix- 
ed with , and hidden in it , there fucceeds a 
green. And this at firft is much inclined to 
blue, but foon becomes a good green, the on- 
ly unmix'd and lively Colour in this fourth Se- 
ries. For as, it verges towards the yellow, it 
begins to interfere with the Colours of the fifth 
Series , by whofe mixture the fucceeding yel- 
low and red are very much diluted and made 
dirty, efpecially the yellow, which being the 
v/eaker Colour is fcarce able to iTiew it felf. 

After 



204 O P T I C K S. 

After this the feveral Series interfere more and 
more, and their Colours become more apd more 
intermix'd, till after three or four more revo- 
lutions ( in which the red and blue predominate 
by turns) all forts of Colours are in all places 
pretty equally blended, and compound an even 
whitenefs. 

And fmce by the 15th Obfervation the Rays 
endued with one Colour are tranfmitted, where 
thofe of another Colour are reflected, the reafon 
of the Colours made by the tranfmitted Light in 
the 9th and 20th Obfervations is from hence 
evident. 

If not only the Order and Species of thefe 
Colours, but alfo the precife thicknefs of the 
Plate, or thin Body at which they are exhibited, 
be defired in parts of an Inch, that may be alfo 
obtained by affiftance of the 6th or i6th Obfer- 
vations. For according to thofe Obfervations 
the thicknefs of the thinned Air, which be- 
tween two GlalTes exhibited the moil luminous 

fjarts of the firfl fix Rings were ^7^^ -^^ 

-4 — —1— — 1— —V- parts of an Inch, 

178000 178000^ 178000^ 178000 -I 

Suppofe the Light refle(5ted moll copioufly at 
thefe thicknefles be the bright citrine yellow, 
or confine of yellow and orange, and thefe thick- 
nefles will be Fa, Fyu, Fr, F|, Fo, F7. And 
this being known, it is eafy to determine what 
thicknefs of Air is reprefented by G(p, or by any 
other difl:ance of the Ruler from A H. 

But farther, fince by the loth Obfervation the 
thicknefs of Air was to the thicknefs of Water, 

which 



BOOK 11. 205 

which between the fame GlaiTes exhibited the 
fame Colour, as 4 to 3, and by the 21ft Obfer- 
vation the Colours of thin Bodies are not varied 
by varying the ambient Medium j the thick- 
nefs of a Bubble of Water, exhibiting any Co- 
lour, will be J of the thicknefs of Air produ- 
cing the fame Colour. And fo according to 
the fame loth and 21ft Obfervat ions, the thiok- 
nefs of a Plate of Glafs, whofe Refradion of 
the mean refrangible Ray, is meafured by the 
proportion of the Sines 31 to 20, may be \° of 
the thicknefs of Air producing the fame Co- 
lours; and the lijce of other Mediums. I do 
not affirm , that this proportion of 20 to 3 r, 
holds in all the Rays ; for the Sines of other 
forts of Rays have other Proportions. But the 
differences of thofe Proportions are fo little 
that I do not here confider them. On thefe 
Grounds I have compofed the following Table, 
wherein the thicknefs of Air, Water, and Glafs, 
at which each Colour is mofl intenfe and fpeci- 
fick, is exprelfed in parts of an Inch divided in- 
to ten hundred thoufand equal parts. 



• me 



2o6 



O P T I C K a 



I'he thicknefs of colour d Plates and Particles of 



-^ 



Their Colours of the 
4kft Order, *\ 



^Very black 

Black 

Beginning of 
Black 

Blue 

White 
I Yellow 

Orange 
vRed 



r Violet 

V Indigo 

A Blue 

Of thcfecond Order, J Green 
Alellow 
y Orange 
/ Bright red 
L Scarlet 



of the third Order,< 



Purple 

Indigo 

Blue 

Green 

Yellow 

Red 

Bluifh red 

Bluifli green 
Green 

Yellowiih green 
Red 

Ofihe fifth Order, {Gre^eniih blue 

-rvr 1 r 1- « J TGreenifli blue 
Of the fixth Order, \^q^ 

of the fevemh Or-rGreeniih blue 
der, (.Ruddy white 



of the fourth Order,* 



^ Jir. 


Water. 


Ghfs. 


1 


J 


J-' 


1 


T 


^ [ 


I 


} 


2 a 




+ 


Tr 


2 


Ij- 


It 


^1 


I'r 


lir 


5t 


3^ . 


3f 


7^ 


5f 


41 


8 


6 


5t 


9 


H 


5t- 


II*- 


81- 


7t 


li^ 


^f 


8tt 


14 


loi- 


9 


i5t 


11^ 


^t 


16} 


I2| 


lof 


17^ 


1? 


ii> 


i8f 


'3^ 


u^ 


i9f 


i+i 


12f 


21 


i5i 


i3t^ 


22t'- 


i6± 


147 


23?- 


T-lVo 


I5t',- 


^51 


18-,^, 


16^ 


27^ 


20.1 


i7t 


^9. 


^4 


1%^ 


1L_ 


24 


20} 


34 


ijf 


22 


5 54 


2cr; 


2Z^ 


3^ 


27 


237- 


Jf7_ 




2<5 


4<? 


34t 


/-9i 


52f 


391- 


34 


5H 


44 


38 


^5 


48} 1 


42 


71 


557 
57|- 


45t 


77 


49f 



Now 



BOOK IL 20 j 

• Now if this Table be compared with the 6th 
Scheme, you will there fee the conftitntion of 
each Colour, as to its Ingredients, or the ori- 
ginal Colours of which it is compounded, and 
dience be enabled to judge of its Intenfenefs or 
Imperfection ; which may fuffice in explication 
of the 4th and i8th Obfervations, unlefs it be 
farther delired to delineate the manner how 
the Colours appear, when the two Objed;-glaf- 
fes are laid upon one another. To do which, 
let there be defcribed a large Arc of a Circle, 
and a ftreight Line which may -touch that Arc, 
and parallel to that Tangent feveral occult 
Lines, at fuch diftances from it, as the Num- 
bers fet againft the feveral Colours in the Ta- 
ble denote. For the Arc, and its Tangent, will 
reprefent the Superficies of the Glalles termi- 
nating the interjacent Air; and the places where 
the occult Lines cut the Arc will (how at what 
diftances from the center, or Point of contadl, 
each Colour is refiedled. 

There are.alfo other Ufesof this Table: For 
by its afiirtance the thicknefs of the Bubble in 
the 19th Obfervation was determin'd by the Co- 
lours which it exhibited. And fo the-bignefs of 
the parts of natural Bodies may be conje- 
diured by their Colours, as ihall be hereafter 
fhewn. Alfo, if two "or more very thin Plates 
be laid one upon another, fo as to compofe one 
Plate equalling them all in thicknefs, the refult- 
ing Colour may be hereby determin'd. For in- 
flance, Mr. Hook obferved, as is mentioned in 
his Micrograpkia^ that a faint yellow Plate of 
Miijccoy Glafs laid upon a bli^e one, conftituted 

a very 



2o8 O P T I C K S. 

a very deep purple. Tke yellow of the firfl Or- 
der is a faint one, and the thicknefs of the Plate 
exhibiting it, according to the Table is 42, to 
which add 9, the thicknefs exhibiting blue of 
the fecond Order, and the Sum will be 13I, 
which is the thicknefs exhibiting the purple of 
the thir4 Order. 

To explain, in the next place, the circum- 
ftances of the 2d and 3d Obfervations 5 that is, 
how the Rings of the Colours may ( by turning 
the Prifms about their common Axis the con- 
trary way to that expreffed in thofe Obferva- 
tions ) be converted into white and black Rings, 
and afterwards into Rings of Colours again, the 
Colours of each Ring lying now in an inverted 
order; it muft be remember'd, that thofe Rings 
of Colours are dilated by the obliquation of the 
Rays to the Air which intercedes the GlalTes, 
and that according to the Table in the 7th Ob- 
fervation, their Dilatation or Increafe of their 
Diameter is mofl manifeft and fpeedy when 
they are obliquefl:. Now, the Rays of yellow 
being more refra(5led by tne firft Superficies of 
the faid Air than thofe of red, are thereby 
made more oblique to the fecond Superficies, 
at which they are refieded to produce the co- 
lour'd Rings, and confequently the yellow Cir- 
cle in each Ring will be more dilated than the 
red ; and the Excefs of its Dilatation will be fo 
much the greater, by how much the greater is 
the obliquity of the Rays, until at laft it be- 
come of equal extent with the red of the fame 
Ring. And for the fame reafon the green, blue 
and violet, will be alfo fo much dilated by the 

ftill. 



BOOK II. 209 

iibill greater obliquity of their Rays, as to be- 
come all very nearly of equal extent with the 
red, that is, equally diltant from the center of 
the Rings, And then all -the Colours of the 
fame Ring mull be coincident, and by their 
mixture exhibit a white Ring. And thefe white 
Rings muft have black and dark Rings between 
them, becaufe they do not fpread and interfvire 
with one another, as before. And for that rea- 
fon alfo they mufl become diftindler, and vifible 
to far greater numbers. But yet the violet be- 
ing obliqueft will be fomething more dilated, 
in proportion to its extent, than the other Co- 
lours, and fo very apt to appear at the exterior 
Verges of the white. 

Afterwards, by a greater obliquity of the 
Rays, the violet and blue become more fenfibly 
dilated than the red and yellow, and fo being 
farther removed from the center of the Rines, 
the Colours muft emerge out of the white in- an 
order contrary to that which they had before; 
the violet and blue at the exterior Limbs of 
each Ring, and the red and yellow at the in- 
terior. And the violet, by reafon of the great- 
eft obliquity of its Rays, being in proportion 
moft of all expanded, will fooneft appear at 
the exterior Limb of each white Ring, and be- 
come more confpicuous than the reft. And the 
feveral Series of Colours belonging to the feve- 
ral Rings, will, by their unfolding and fpread- 
ing, begin again to interfere, and thereby ren- 
der the Rings lefs diftindt, and not vifible to fo 
great numbers. 

P If 



2IO O P T I C K S. 

If inflead of the Prifms the Objed-glafleS be 
made ufe of, the Rings which they exhibit be- 
come not white and diilindl by the obhquity of 
the Eye, by reafon that the Rays in their paflage 
through that Air which intercedes tne Glafles 
are very nearly parallel to thofe Lines in which 
they were lirft incident on the GlafTes, and con- 
fequently the Rays endued with feveral Colours ^ 
are not inclined one more than another to that 
Air, as it happens in the Prifms. 

There is yet another circumftance of thefe 
Experiments to be confider'd, and that is why 
the black and white Rings which when view'd 
at a diftance appear diftincft, fliould not only be- 
come confufed by viewing them near at hand, 
but alfo yield a violet Colour at both the edges 
of every white Ring. And the reafon is, that 
the Rays which enter the Eye at feveral parts 
of the Pupil, have feveral Obliquities to the Glaf- 
fes, and thofe which are mofl oblique, if confi- 
der'd apart, would reprefent the Rings bigger 
than thofe which are the leaft oblique. Whence 
the breadth of the Perimeter of every white 
Ring is expanded outwards by the obliquefl 
Rays, and inwards by the leafi oblique. And 
this Expanfion is fo much the greater by how 
much the greater is the difference of the Obli- 
quity ; that is, by how much the Pupil is wider^ 
or the Eye nearer to the Glafles. And the 
breadth of the violet muft be mofb expanded, 
becaufe the Rays apt to excite a Senfation of 
that Colour arc mofl oblique to a fecond or 
farther Superficies of the. thinn'd Air at which 
they are rcfiedted, and have alfo the grearefl 

varia- 



BOOK II. 211 

variation of Obliquity, which makes that Co- 
lour fooneft emerge out of the edges of the 
white. And as the breadth of every Ring is 
thus augnaented, the dark Intervals niufl be di- 
minifli'd, until the neighbouring Rings become 
continuous, and are blended, the exteiior iiril, 
and then thofe nearer the center j fo that they 
can no longer be diftinguifh'd apart, but feem to 
conflitute an even and uniform whitenefs. 

Among all the Obfervations there is none ac- 
companied with fo odd circumftances as the 
twenty-fourth. Of thofe the principal are, that 
in thin Plates, v/hich to the naked Eye feem of 
an even and uniform tranfparent whitenefs, 
without any terminations of Shadows, the Re- 
fraction of a Prifm fhould make Rings of Co- 
lours appear, whereas it ufually makes Objedts 
appear colour'd only there where they are ter- 
minated with Shadows, or have parts unequal- 
ly luminous ; and that it fliould make thofe 
Kings exceedingly diftindl and white, although 
it ufually renders Objeds confufed and colour- 
ed. The Caufe of thefe things you will under- 
ftand by confidering, that all the Rings of Co- 
lours are really in tiie Plate, when vie w'd with 
the naked Eye, although by reafon of the great ' 
breadth of their Circumferences they fo much 
interfere and are blended together, that they 
feem to conflitute an uniform whitenefs. But 
when the Rays oafs through the Prifm to the 
Eye, the Orbits of the feveral Colours in every 
Ring are refraded, fome more than others, ac- 
cording to their degrees of Pvcfrangibility : By 
which means the Colours on one fide of the 

P 2 Ring 



212 O P T I C K S. 

Ring (that is in the circumference on one fide of 
its center, ) become more unfolded and dilated, 
and thofe on the othef fide more complicated and 
contraded. And where by a due Refra(3:ion they 
are fo much contradied, that the feveral Rings' 
become narrower than to interfere with one ano- 
ther, they muft appear diftind:, and alfo white, 
if the conftituent Colours be fo much contrad:ed 
as to be wholly coincident. But on the other 
fide, where the Orbit of every Ring is made 
broader by the farther unfolding of its Colours, 
it muft interfere more with other Rings than be- 
fore, and fo become lefs diftind;. 

To explain this a little farther, fuppofe the 
concentrick Circles A V, and B X, [in Fig. 7.] 
reprefent the red and violet of any Order,- 
which, together with the intermediate Colours, 
conllitute any one of thefe Rings. Now thefe 
being view'd through a Prifm, the violet Circle 
B X, will, by a greater Refraction, be farther 
tranllated from its place than the red A V^ and 
fo approach nearer to it on that fide of the Cir- 
cles, towards which the Refractions are made. 
For inftance -, if the red be tranflated to a v, 
the violet may be tranflated to I? x, fo as to ap- 
proach nearer to it at x than before y and if the 
red be farther tranllated to av, the violet may 
be fo much farther tranflated to b x as to con- 
vene with it at X ; and if the red be yet farther 
tranflated to a T, the violet may be ftill fo much 
farther tranflated to /? | as to pafs beyond it at 
§, and convene with it at e and f. And this 
being underllood not only of the red and vio- 
let, but of all the other intermediate Colours, 

and 



BOOK II. 213 

and alfo of every revolution of thofe Colours, 
you will ealily perceive how thofe of the fame 
revolution or order, by their nearnefs at x v 
and T J, and their coincidence at x v, e and J\ 
ought to conftitute pretty diftindt Arcs of Cir- 
cles, efpecially at x v, or at e and f; and that 
they will appear feverally at x Vy and at x v ex- 
hibit whitenefs by their coincidence, and again 
appear feveral at T |, but yet in a contrary or- 
der to that which they had before, and ftill re- 
tain beyond e and f. But on the other fide, 
at a I?, a b, or a l3, thefe Colours mufl: become 
much more confufed by being dilated and fpread 
fo as to interfere with thofe of other Orders. 
And the fame confufion will happen at T | be- 
tween e and f^ if the Refraction be very great, 
or the Prifm very diftant from the Objcdt-glaf- 
fes : In which cafe no parts of the Rings will 
be feen, fave only two little Arcs at e and J\ 
whofe diftance from one another will be aug- 
mented by removing the Prifm flill farther from 
the Objed-glafTes : And thefe little Arcs mult 
be diftindtefl and w^hiteft at their middle, and 
at their ends, where they begin to grow con- 
fufed, they mull be colour'd. And the Colours 
at one end of every Arc mufl be in a contrary 
order to thofe at the other end, by reafon that 
they crofs in the intermediate white ; namely, 
their ends, which verge towards T g, will be 
red and yellow on that fide next the center, 
and blue and violet on the other fide. But 
their other ends which verge from. T J, will on 
the contrary be blue and violet on that fide to- 

P 2 ^ya^ds 



214 O P T I C K S. 

wards the center, and on the other fide red and 
yellow. 

Now as all thefe things follow from the pro- 
perties of Light by a mathematical way of rea- 
foning, fo the truth of them may be manifefted 
by Experiments. For in a dark Room, by view- 
ing thefe Rings through a Prifm, by reflexion 
of the feveral prifmatick Colours, which an 
affiftant caufes to. move to and fro upon a Wall 
or Paper from whence they are reflected, whilft 
the Spe6:ator's Eye, ihe Prifm, and the Objed:- 
glaffes, (as in the 13th Obfervation,) are placed 
Iteadyj the Polition of the Circles made fuc- 
ceifively by the feveral Colours, will be found 
fuch, in refped: of one another, as I have de- 
scribed in the Figures a b x ^0^ or a b x v, or 
a /S I T. And by the fame method the truth of 
the Explications of other Obfervations may be 
examined. 

By what hath been faid, the like Phaenomena 
of Water and thin Plates of Glafs may be un- 
derftood. But in fmall fragments of thofe Plates 
there is this farther obfervable, that where they 
lie flat upon a Table, and are turned about their 
centers whilfl they are view'd through a Prifm, 
they will in fome poflures exhibit Waves of va- 
rious Colours ; and fome of them exhibit thefe 
Waves in one or two Pofitions only, but the 
mofc of them do in all Pofitions exhibit them, 
and make them for the mofl part appear al- 
mioft all over the Plates. The reafon is, that 
the Superficies of fuch Plates are not even, but 
have many Cavities and Swellings, which, how 
fhallow foever, do a little vary the thicknefs of 

th^ 



BOOK II. 215 

tlie Plate. For at the feveral fides of thofe Ca- 
vities, for the Reafons newly defcribed, there 
ought to be produced Waves in feveral po- 
llures of the Prifm. Now though it be but 
fome very fmall and narrower parts of the Glafs, 
by which thefe Waves for the niofl part are cau- 
fed, yet they may feem to extend themfelves 
over the whole Glafs, becaufe from the narrow- 
eft of thofe parts there are Colours of feveral 
Orders, that is, of feveral Rings, confufedly re- 
fleded, which by Refraction of the Prifm are 
unfolded, feparated, and, according to their 
degrees of Refraction, difperfed to feveral pla- 
ces, fo as to conftitute fo many feveral Waves, 
as there were divers orders of Colours promifcu- 
oufly reflected from that part of the Glafs. 

Thefe are the principal Phasnomena of thin 
Plates or Bubbles, whofe Explications depend 
on the properties of Light, which I have here- 
tofore deliver'd. And thefe you fee do necef- 
farily follow from them, and agree with them, 
even to their very leaft circumftancesj and not 
only fo, but do very much tend to their proof. 
Thus, by the 24th Obfervation it appears, that 
the Rays of feveral Colours, made as well by thin 
Plates or Bubbles, as by Refradions of a Prifm, 
haye feveral degrees of Refrangibility j where- 
by thofe of each order, which at the reflexion 
from the Plate or Bubble are intermix'd with 
thofe of other orders, are feparated from them 
by Refraction, and aflbciated together fo as to 
become vifible by themfelves like Arcs of Cir- 
cles. For if the Rays were all alike refrangi- 
ble, 'tis impofiible that the whitenefs, which 

P 4 to 



2i6 O P T I C K S. 

to the naked Senfe appears uniform, fhould by 
Refraction have its parts tranfpofed and ranged 
into thofe black and white Arcs. 

It appears alfo that the unequal Refradlions 
of difforin Rays proceed not from any contin- 
gent irregularities ; fuch as are Veins, an uneven 
Polifh, or fortuitous Polition of the Pores of 
Glafs ; unequal and cafual Motions in the Air 
or /Ether, the fpreading, breaking, or dividing 
the fame Ray into many diverging parts ; or the 
like. For, admitting any fuch irregularities, 
it v^ould be impoiTible for Refractions to render 
ihofe Rings fo very diflincft, and well defined, 
as they do in the 24th Obfervation. It is ne^ 
cefTary therefore that every Ray have its proper 
and conftant degree of Refrangibility connate 
with it, according to which its refraction is ever 
juflly ^nd regularly perform'd^ and that feveral 
flays have feveral of thofe degrees. 

And what is faid of their Refrangibility may 
be alfo underflood of their Reflexibility, that is, 
of their Difpofitions to be refle<^ed, fome at a 
greater, and others at a lefs thicknefs of thin 
Plates or Bubbles j namely, that thofe Difpofi- 
tions are alfo connate with the Rays, and im- 
mutable ; a^ may appear by the 13 th, 14th, and 
J 5 th Obfervations, compared with the fourth and 
eighteenth. 

By the precedent Obfervations it appears al- 
fo, that whitenefs is a diihmilar mixture of all 
polours, and that Light is a mixture of Rays 
endued with all thofe Colours. .For, confider- 
ing the multitude of the Rings of Colours in 
jhe ^d^ I2th5 and 24th Obfervations, itismani- 
"■■^ ■ ; feft, 



BOOK 11. 217 

feft, that although in the 4th and i8th Obfer- 
vations there appear no more than eight or 
jiine of thofe Rings, yet there are really a far 
greater number, which fo much interfere and 
mingle with one another, as after thofe eight 
or nine revolutions to dilute one another whol- 
ly, and conllitute an even and fenfibly uniform 
whitenefs. And confequently that whitenefs 
muft be allow'd a mixture of all Colours, and 
the Light which conveys it to the Eye muft 
be a mixture of Rays endued with all thofe Co- 
lours. 

But farther J by the 24th Obfervation it ap- 
pears, that there is a conftant relation between 
Colours and Refrangibility ; the moft refrangi- 
ble Rays being violet, the leaft refrangible red, 
and thofe of intermediate Colours having pro- 
portionably intermediate degrees of Refrangibi- 
lity. And by the 13th, 14th, and J5th Obfer- 
vations, compared with the 4th or i8th, there 
appears to be tlie fame conftant relation be- 
tween Colour and Reflexibility ; the violet be- 
ing in like circumftances refleded at leaft thick- 
nelfes of any thin Plate or Bubble, the red at 
greateft thicknelTes, and the intermediate Co- 
lours at intermediate thicknefles. Whence it 
follows, that the colorifick Difpofitions of Rays 
are alfo connate with them, and immutable^ and 
by confequence, that all the Produdions and 
Appearances of Colours in the World are de- 
rived, not from any phyfical Change caufed in 
Light by • Refradion or Reflexion, but only 
Irom the various Mixtures or Separations of 
|lays, by virtue of their different Refrangibility 

or 



-^ 



218 



O P T I C K S. 



or Reflexibility. And in this refped the Scicncd 
of Colours becomes a Speculation as truly ma- 
thematical as any other part of Opticks. I mean, 
fo far as they depend on the Nature of Light, 
and are not produced or alter'd by the Power 
v of Imagination, or by ilriking or preffing the 
Eye. 




THE 




THE 

SECOND BOOK 



O F 



OPTICKS. 



PART III. 



Of the permanejit Colours of natural Bo- 
dies^ and the Analogy between them and 
the Colours of thiii tranfparent Plates* 

AM now come to another part of 
this Defign, which is to confider how 
the PhiEnomena of thin tranfparent 
Plates fland related to thofe of all o- 
ther natural Bodies. Of thefe Bodies I have al- 
ready told you that they appear of divers Co- 
lours, 




220 O P T I C K S. 

lours, accordingly as they are difpofed to refled: 
moft copiouily the Rays originally endued with 
thofe Colours. But their Conflitutions, where- 
by they refied: fome Rays more copiouily than 
others, remain to be difcover'd ; and thefe I lliall 
endeavour to manifeft in the following Propo- 
iitions. 



P R O p. I. 

*ith'ofe Superficies of t ran/ parent Bodies refieEi the 
greatejl quantity of Lights which have the great- 
eft refraBing Power ^ that is, which i7itercede 
Mediums that differ mofi in their refraBiije Den- 
Jities. And in the Confines of equally refraBing 
Mediums there is no Kefiexion. 

TH E Analogy between Reflexion and Re- 
fradion will appear by confidering, that 
when Light paffeth obliquely out of one Medi- 
um into another which refracts from the per- 
pendicular, the greater is the difference of their 
refradive Denfuy, the lefs Obliquity of Inci- • 
dence is requifite to caufe a total Reflexion, 
For as the Sines are which meafure the Refra- 
(Ttion, fo is the Sine of Incidence at which the 
total Reflexion begins, to the Radius of the 
Circle ; and confequently that Angle of Inci- * 
dence is leaft where there is the greateft difl^e- 
rence of the Sines; Thus in the paffing of 
Light out of Water into Air, where the Refra- 
ction is meafured by the Ratio of the Sines 3 to 
4, the total Reflexion begins when the Angle 
of Incidence is about 48 Degrees 35 Minutes, 
'^ In 



BOOK II. ill 

Iti pafling out of Glafs into Air, where the Re- 
fradiion is meafured by the Ratio of the Sines 
20 to 31, the total Reflexion begins when the 
Angle of Incidence is 40 Degrees 10 Minutes; 
and fo in paffing out of Cryftal, or more flrong- 
ly refrading Mediums into Air, there is ftill a lefs 
obliquity requifite to caufe a total reflexion. 
Superficies therefore v/hich refrad; mofl: do 
fooneft refled: all the Light which is incident 
on them, and fo muft be allowed moft flrongly 
reflexive. 

But the truth of this Propofition will farther 
appear by obferving, that in the Superficies in- 
terceding two tranfparent Mediums, (fuch as are' 
Air, Water, Oil, common Glafs, Cryftal, me- 
talline Glafies, Ifland Glafl^es, white tranfparent 
Arfenick, Diamonds, ^c.) the Reflexion is 
ftronger or weaker accordingly, as the Super- 
ficies hath a greater or lefs refrading Power. 
For in the Confine of Air and Sal-gem 'tis 
ftronger than in the Confine of Air and Water, 
and ftill ftronger in the Confine of Air and .com- 
mon Glafs or Cryftal, and ftronger in the Con- 
fine of Air and a Diamond. If any of thefe, 
and fuch like tranfparent Solids, be immerged 
in Water, its Reflexion becomes much weak- 
er than before j and ftill weaker if they be im- 
merged in the more ftrongly refrading Liquors 
of well rectified Oil of Vitriol or Spirit of Tur- 
pentine. If Water be diftinguifli'd into two 
parts by any imaginary Surface, the Reflexion 
in the Confine of thofe two parts is none at all. 
In the Confine of Water and Ice 'tis very little ; 
in that of Water and Oil 'tis fomething greater; 

la 



222 O P T I C K S. 

in that of Water and Sal-gem ftill greater ; and 
in that of Water and Glafs, or Cryftal, or other 
denfer Subftances ftill greater, accordingly as 
thofe Mediums differ more or lefs in their re- 
frading Powers. Hence in the Confine of com- 
mon Glafs and Cryftal, there ought to be a 
weak Reflexion, and a ftronger Reflexion in 
the Confine of common and metalline Glafs; 
though I have not yet tried this. But in the 
Confine of two Glafies of equal denfity, there 
is not any fenfible Reflexion ; as was fliewn in 
the firft Obfervation. And tlie fame may be 
underftood of the Superficies interceding two 
Cryftals, or two Liquors, or any other Sub- 
ftances in which no Refradion is caufed. So 
then the reafon why uniform pellucid Mediums 
(fuch as Water, Glafs, or Cryftal,) have no fen- 
fible Reflexion but in their external Superficies, 
where they are adjacent to other Mediums of 
a diflferent denfity, is becaufe all their conti- 
guous parts have one and the fame degree of 
denfity. 

Prop. II. 

^he leajl parts of almojl all jtatiiral Bodies are 
in fome meajure tranfparent : And the Opa- 
city of thofe Bodies arifeth from the multi- 
tude of "Reflexions caufed in their intertial 
Parts, 

'Tp HAT this is fo has been obferved by o- 

-*• thers, and will eafily be granted by them 

that have been converfant with Microfcopes. 

And it may be alfo tried by applying any fub- 

flancc 



BOOK JL 223 

ftance to a hole through which fome Light is 
immitted into a dark Room. For how opake 
foever that Subftance may feem in the opea 
Air, it will by that means appear very manifeft- 
ly tranfparent, if it be of a fufficient thiniiefs. 
Only white metalline Bodies miift be excepted, 
which by reafon of their exceffive denfity feem 
to refled: almoft all the Light incident on their 
firft Superficies j unlefs by folution in Menftru- 
ums they be reduced into very fmall Particles, 
and then they become tranfparent. 

Prop. IIL 

Between the parts of opake mid colour d Bodies 
are many Spaces^ either empt)\ or repleniJUd 
with Mediians of other DenfitieSy as Water 
between the tingijig Corpufcles wherewith a- 
ny Liquor is impregnated ^ Air between the 
aqueous Globules that confiitute Clouds or Mijh\ 
and for the mofl part Spaces loid of both Air 
and Water ^ but yet perhaps not wholly ^coid of 
all Subjlance^ between the parts of hard Bo- 
dies, 

' I ^ H E truth of this Is evinced by the two 
-^ precedent Propofitions : For by the fe- 
cond Propofition there are many Reflexions 
made by the internal parts of Bodies, which, by 
the firll Propoiition, would not happen if the 
parts of thole Bodies were continued without 
any fuch Interftices between them ; becaufe Re- 
flexions are caufed only in Superficies, which 
intercede Mediums of a differing denfity, by 
'Frop, I. 

• ^ Buc 



224 O P T I C K S. 

But farther, that this difcontinuity of parts 
is the principal Caufe of the opacity of Bodies, 
will appear by confidering, that opake Subftan- 
ces become tranfparent by filling their Pores 
with any Subftance of equal or almoft equal den- 
fity with their parts. Thus Paper dipped in 
Water or Oil, the O cuius Mundi Stone fteep'd 
in Water, Linnen Cloth oiled or varniih'd, and 
many other Subilances foaked in fuch Liquors 
as will intimately pervade their little Pores, be- 
come by that means more tranfparent than other- 
wife ; fo, on the contrary, the mofh tranfparent 
Subftances may, by evacuating their Pores, or 
feparating their parts, be render'd fufficiently o* 
pake ; as Salts or wet Paper, or the Oculus Mun- 
di Stone by being dried, Horn by being fcraped, 
Glafs by being reduced to Powder, or otherwife 
flawed; Turpentine by being ftirred about with 
Water till they irdx imperfectly, and Water by 
being form'd into many fmall Bubbles, either a- 
lone in the form of Froth, or by fliaking it to- 
gether with Oil of Turpentine, or Oil Olive, or 
with fome other convenient Liquor, with which 
it will not perfectly incorporate. And to the in- 
creafe of the opacity of thefe Bodies, it condu- 
ces fomething, tliat by the 23d Obfervation the 
Reflexions of very thin tranfparent Subftances are 
conliderably ftronger than thofe made by the 
faipe Subftances of a greater thicknefs, 



Prop* 



BOOK IL 225 

Prop. IV. 

The Farts of Bodies and their Interftices mi/fl not 
be lefs than of feme definite bignefs^ to render^ 
them opake and colour d. 

■p.OR the opakeft Bodies, if their parts be 
■*- fubtilly divided, (as Metals, by being diflbl- 
ved in acid Menftruums, ^c^ become perfect- 
ly tranfparent. And you may alfo remember, 
that in the eighth Obfervation there 'was no 
fenfible reflexion at the Superficies of the Ob- 
ied-glaffes, where they were very near one an- 
other, though they did not ablblutely touch. 
And in the 1 7th Obfervation the • Reflexion of 
the Water- bubble where it became thinriell was 
almofl infenfible, fo as to caufe very black Spots 
to appear on the top of the BubblCj by the want 
of reflected Light. 

On thefe grounds I perceive it is that Water, 
Salt, Glafs, Stones, and fuch like Subftances, 
are tranfparent. For, upon divers Confidera- 
tions, they feem to be as full of Pores or Inter- 
ftices between their parts as other Bodies are, 
but yet their Parts and Interftices to be too 
fmall to caufe Reflexions in their common Sur- 
faces. 



Q^ Prop. 



226 O P T I C K S. 

P R O p. V. 

^he tranfparcnt farts of Bodies, according to their 
Je-veral Jizes^ reJieEl Rays of one Colour^ and 
traifmit thofe of another y on the fame grounds 
that thin Plates or Bubbles do refeB or tranfmit 
thofe Rays, Atid this, I take to be the ground of 
all'their Colours. 

*P O R if a thinn'd or plated Body, which 
-■- being of an even thicknefs, appears all o- 
ver of one uniform Colour, fliould be flit into 
Threads, or broken into Fragments, of the fame 
thicknefs with the Plate j I fee no reafon why 
every Thread or Fragment fhould not keep its 
Colour, and by confequence why a heap of thofe 
Theads or Fragmmts fliould not conflitute a 
Mafs or Powder of the fame Colour, which the 
Plate exhibited before it was broken. And the 
parts of all natural Bodies being like fo many 
Fragments of a Plate, muft on the fame grounds 
exhibit the fame Colours. 

Now, that they do fo will appear by the affi- 
nity of their Properties. * The finely colour'd 
Feathers of fome Birds, and particularly thofe 
of Peacocks Tails, do, in the very fame part of 
the Feather, appear of feveral Colours in feveral 
Pofitions of the Eye, after the very fame man- 
ner that thin Plates were found to do in the 
7th and 1 9th Obfervations, and therefore their 
Colours arife from the thinnefs of the tranfpa- 
rent parts of the Feathers; that is, from the 
flendernefs of the very fine Hairs, or Capilla- 
menta^ which grow put of the fides of the 

groifer 



BOOK II. 227 

grofler lateral Branches or Fibres of thofe Fea- 
thers. And to the fame purpofe it is, that the 
"Webs of fome Spiders, by being fpun very fine, 
have appeared colour'd, as fome have oblerv'd, 
and that the colour'd Fibres of fome Silks, by 
varying the Pofition of the Eye, do vary their 
Colour. Alfo the Colours of Silks, Cloths, 
and other Subftances, which Water or Oil can 
intimately penetrate, become more faint and 
obfcure by being immerged in thofe Liquors, 
and recover their Vigor again by being dried ; 
much after the manner declared of thin Bodies 
in the loth and 21ft Obfervations. Leaf-Gold, 
fome forts of painted Glafs, the Infufion of 
Lignutn Nephritiaun, and fome other Subilan-' 
ces, refledl one Colour, an(i tranfmit another;, 
like thin Bodies in the 9th and 20th Obferva- 
tions. And fome of thofe colour'd Powder5 
which Painters ufe, may have their Colours a 
little changed, by being very elaborately and 
finely ground. Where I fee not what can be 
juftly pretended for thofe changes, befides the 
breaking of their parts into lefs parts by that 
contrition, after the fame manner that the Co- 
lour of a thin Plate is changed by varying its 
thicknefs. For which reafon alfo it is that the 
colour'd Flowers of Plants and Vegetables, by 
being bruifed, ufually become more tranfparenz 
than before, or at leafl in fome degree or o- 
ther change their Colours. Nor is it much lefs 
to my purpofe, that, by mixing divers Liq^uors, 
very odd and remarkable Produd:ions and 
Changes of Colours may be effected, of which 
no caufe can be more obvious and rational than 

Q^ that. 



228 O P T I C K S. 

tha:t the faiine Corpufcles of one Liquor da vari- 
oufly ad upon or unite with the tinging Corpufcles 
of another, fo as to make them fwell, or fhrink, 
( whereby not only their bulk but their denfity 
alfo may be changed,) or to divide them into 
fmaller Corpufcles, (whereby a colour'd Liquor 
may become tranfparent,) or to make many of 
them affociate into one clufter, whereby two 
tranfparent Liquors may compofe a colour'd one. 
For we fee how apt thofe faiine Menftruums are 
to penetrate and diffolve Subftances to which 
they are applied, and fome of them to precipi- 
tate what others diilblve. In like manner, if we 
confider the various Phaenomena of the Atmo- 
fphere, we may obferve, that when Vapours are 
iirft raifed, they hinder not the tranfparcncy of 
the Air, being divided into parts too fmall to 
caufe any Reflexion in their Superficies. But 
when in order to compofe drops of Rain they 
begin to coalefce and conflitute Globules of all 
intermediate lizes, thofe Globules, when they 
become of a convenient fize to refle6t fome Co- 
lours and tranfmic others, may conftitute Clouds 
of various Colours according to their fizes. And 
I fee not what can be rationally conceived in fo 
tranfparent a Subftance as Water for the produ- 
ction of thefe Colours, befides the various fizes 
of its fluid and globular Parcels. 



Prop, 



BOOK 11. 229 

Prop. VI. 

^he parts of Bodies 011 ivhich their Colours depend ^ 
are denjer than the Medium which pervadet 
their Interjiices, 

np HIS will appear by confidering, that the 
-■" Colour of a Body depends not only on 
the Rays which are incident perpendicularly 
on its parts, but on thofe alfo which arc inci- 
dent at all other Angles. And that according 
to the 7th Oblervation, a very little variation 
of obliquity will change the refled:ed Colour, 
where the thin Body or fmall Particle is rarer 
than the ambient Medium, infomuch that fuch 
a fmall Particle will at diverfly oblique Inci- 
dences refledl all forts of Colours, in fo great a 
variety that the Colour refuking from them all, 
confufedly refled:ed from a heap of fuch Parti- 
cles, muft rather be a white or grey than any 
other Colour, or at beft it muft be but a very 
imperfecft and dirty Colour. Whereas if the 
thin Body or fmall Particle be much denfer than 
the ambient Medium, the Colours, according to 
the 19th Obfervation, are fo little changed by 
the variation of obliquity, that the Rays which 
are refled;ed leafl obliquely may predominate 
over the feft, fo much as to caufe a heap of fuch 
Particles to appear very intenfely of their Co- 
lour. 

It conduces alfo fomething to the confirma- 
tion of this Propolition, that, according to the 
22d Obfervation, the Colours exhibited by the 
denfer thin Body within the rarer,' are more 

0^3 ^ brisk 



130 O P t I C K S. 

brisk than thofe exhibited by the rarer within the 
denfer. 

I Prop. VII. 

*the bignefs of the component parts of natural Bo- 
dies may be conjellured by their Colours. 

FO R fince the parts of thefe Bodies, by 
Frop, 5. do mofl probably exhibit the 
fame Colours with a Plate of equal thicknefs, 
provided they have the fame refradiive denlity ; 
and fince their parts feem for the mcft part to 
have much the fame dehfity with Water or 
Glafs, as by many circumftances is obvious to 
colledt J to determine the fizes of thofe parts, 
you need only have recourfe to the precedent 
Tables, in which the thicknefs of Water or 
Glafs exhibiting any Colour is exprefled. Thus 
if it be defired to know the diameter of a Cor- 
p.ufcle, which being of equal denlity with Glafs 
ihall refled: green of the third Orders the Num- 
ber 165 (hews it to be ^-^ parts of 'an Inch. 
^ I 0000 A 

The greatefl: difficulty is here to know of 
what Order the Colour of any Body is. And 
for this end we muft have recourfe to the 4th 
and 1 8th Obfervations ; from whence may be 
coUedted thefe particulars. 

■Scarlets y and other reds^ oranges y and yel~ 
JowSy if they be pure and intenfe, are mofl pro- 
bably of the fecond order. Thofe of fhe firfl 
and third order alfo may be pretty goodj only 
the yellow of the firfl order is faint, and the 

_ orange 



BOOK II. 231 

orange and red of the third Order have a great 
Mixture of violet and bkie. 

There may be good Greens of the fourth Order, 
but the pureft are of the third. And of this 
Order the green of all Vegetables feenis to be, 
partly by reafon of the Intenfenefs of their Co- 
lours, and partly becaufe when they wither fome 
of them turn to a greenifh yellow, and others 
to a more perfed: yellow or orange, or perhaps 
to red, paiTing firft through all the aforefaid in- 
termediate Colours. Which Changes feem to 
be effected by the exhaling of the Moifture 
which may leave the tinging Corpufcles more 
denfe, and fomething augmented by the Accre- 
tion of the oily and earthy Part of that Moifture. 
Now the green, without doubt, is of the fame 
Order with thofe Colours into which it changeth, 
becaufe the Changes are gradual, and thofe Co- 
lours, though ufually not very full, yet ar& 
often too full and lively to be of the fourth 
Order. 

Blues and Purples may be either of the fe- 
cond or third Order, but the beft are of the 
third. Thus the Colour of Violets feems to be 
of that Order, becaufe their Syrup by acid Li- 
quors turns red, and by urinous and alcaiizate 
turns green. For fince it is of the Nature of 
Acids to diffolve or attenuate, and of Alcalies 
to precipitate or incrailate, if the Purple Co^ 
lour of the Syrup was of the fecond Order, an 
acid Liquor by attenuating its tinging Cor- 
pufcles would change it to a red of the in ft Or- 
der, and an Alcali by incralTating them would 
change it to a green of the fecond Order ; 

Qjj. which 



232 O P T I C K S. 

which red and green j efpecially the green, feem 
too imperfed: to be the Colours produced by 
thefe Changes. But if the faid Purple be fup- 
pofed of the third Order, its Change to red of the 
fecond, and green of the third, may without any 
Inconvenience be allow'd. 

If there be found any Body of a deeper and lefs 
reddifh Purple than that of the Violets, its Colour 
moft probably is of the fecond Order. But yet 
there being no Body commonly known whofe Co- 
lour is conftantly more deep than theirs, I have 
made ufe of their Name to denote the deepeft and 
leaft reddilh Purples, fuch as manifeftly tranfccnd 
their Colour in purity. 

The blue of the firft Order, though very faint 
and little, may poffibly be the Colour of fome 
Subftances j and particularly the azure Colour 
of the Skies feems to be of this Order. For all 
Vapours when they begin to condenfe and coa- 
lefce into fmall Parcels, become firft of that Big- 
nefs, whereby fuch an Azure muft be reflected be- 
fore they can conftitute Clouds of other Colours. 
And fo this being the firft Colour which Vapours 
begin to refled, it ought to be the Colour of the 
fineft and moft tranfparent Skies, in which Va- 
pours are not arrived to that Grofliiefs requifite to 
refled: other Colours, as we find it is by Expe- 
rience. 

JVhitenefs, if moft intenfe and luminous, is 
that of the firft Order, if lefs ftrong and lumi- 
nous, a Mixture of the Colours of feveral Or- 
ders. Of this laft kind is the Whitenefs of 
Froth, Paper, Linnen, and moft white Sub- 
ftances j of the former I reckon that of white 

Metals 



BOOK II. 233 

Metals to be. For whilft the denfell of Metals, 
Gold, if foliated, is tranfparent, and all Metals 
become tranfparent if dilfolved in Menftriiums 
or vitrified, the Opacity of white Metals ari- 
feth not from their Denfity alone. They be- 
ing lefs denfe than Gold would be more tranf- 
parent than it, did not fome other Caufe con- 
cur with their Denfity to make them opake. 
And this Caufe I take to be fuch' a Bignefs of 
their Particles as fits them to refledl the white of 
the firft order. For, if they be of other Thick- 
nefi!es they may refled: other Colours, as is ma- 
nifeft by the Colours which appear upon hot 
Steel in tempering it, and fometimes upon the 
Surface of melted Metals in the Skin or Scoria 
which arifes upon them in their cooling. And 
as the white of the firfl order is the Itrongefl 
which can be made by Plates of tranfparent 
Subftances, fo it ought to be ftronger in the 
denfer Subftances of Metals tlian in the rarer 
of Air, Water, and Glafs. Nor do I fee but 
that metallick Subftances of fuch a Thicknefs as 
may fit them to reflect the white of the firft or- 
der, may, byreafon of their great Denfity (ac- 
cording to the Tenor of the firft of thefe Pro- 
pofitions) refled: all the Light incident upon 
them, andfo be as opake and fplendent as it's 
poflible for any Body to be. Gold, or Copper 
mix'd with lefs than half their Weight of Silver, 
or Tin, or Regulus of Antimony, in fufion, or 
amalgamed with a very little Mercury, become 
white J which fhews both that the Particles of 
white Metals have much more Superficies, and 
fo are fmaller, than thofe of Gold and Copper, 

and 



234- O P T I C K S. 

and alfo that they are fo opake as not to fuflef 
the Particles of Gold or Copper to fhine through 
them. Now it is fcarce to be doubted, but 
that the Colours of Gold and Copper are of 
the fecond or third order, and therefore the 
Particles of white Metals cannot be much big- 
ger than is requifite to make them reflect the 
white of the firft order. The Volatility of Mer- 
cury argues that they are not much bigger, 
nor may they be much lefs, left they lofe their 
Opacity, and become either tranfparent as they 
do when attenuated by Vitrification, or by Solu- 
tion in Menftruums, or black as they do when 
ground fmaller, by rubbing Silver, or Tin, or 
Lead, upon other Subftances to draw black 
Lines. The firft and only Colour which white 
Metals take by grinding their Particles fmaller, 
is black, and therefore their white ought to be 
that which borders upon the black Spot in the 
Center of the Rings of Colours, that is, the 
white of the firft order. But, if you would 
hence gather the Bignefs of metallick Particles, 
you muft allow for their Denfity. For were 
Mercury tranfparent, its Denfity is fuch that 
the Sine of Incidence upon it ( by my Compu- 
tation) would be to the Sine of its Refraction, 
as 7 1 to 20, or 7 to 2. And therefore'the Thick- 
nefs of its Particles, that they may exhibit the 
fame Colours with thofe of Bubbles of Water, 
ought to be lefs than the Thicknefs of the 
Skin of thofe Bubbles in the Proportion of 2 
to 7. Whence it's pofiible, that the Particles 
of Mercury m.ay be as little as* the Particles of 

fome 



BOOK II. 235 

(ome tranfparent and volatile Fluids, and yet 
refled the white of the firft order. 

Laftly, for the produdtion of blacky the Cor- 
pufcles mufl be lefs than any of thofe which ex- 
hibit Colours. For at all greater fizes there is 
too much Light reflected to conftitute this Co- 
lour. But if they be fuppofed a little lefs than 
is requifite to refled^ the white and very faint 
blue of the firfl order, they will, according to 
the 4th, 8th, i7thand iSthObfervations, refled: 
fo very little Light as to appear intenily black, 
and yet may perhaps varioully refrad it to and 
fro within themfelves fo long, until it happen 
to be ftifled and loft, by which means they will 
appear black in all pofitions of the Eye without 
any tranfparency. And from hence may be under- 
flood why Fire, and the more fubtile diffolver Pu- 
trefaction, by dividing the Particles of Subftan- 
ces, turn them to black, why fmall quantities 
of black Subftances impart their Colour very 
freely and intenfly to other Subftances to which 
they are applied ; the minute Particles of thefe, 
by reafon of their very great number, eaftly o- 
verfpreading the grofs Particles of others ; why 
Glals ground very elaborately with Sand on a 
Copper Plate, 'till it be well poliftVd, mukes 
the Sand, together with what is worn off" from 
the Glafs and Copper, become very black : 
wiiy black Subftances do fooneft of all others 
become hot in the Sun's Light and burn, (which 
Effed: may proceed partly from the multitude 
of Refradions in a little room, and partly from 
the eafy Cominotion of fo very fmall Cor- 
pufcies; ) and why blacks are ufually a little in- 
clined 



236 O P T I C K S. 

clined to a bluifli Colour. For that they are Co 
may be feen by illuminating white Paper by 
Light refie.ded from black Subftances. For the 
Paper will ufually appear of a bluifh white j and 
the reafon is, that black borders on the obfcure 
blue of the order defcribed in the i8th Obferva- 
tion, and therefore refled:s more Rays of that Co- 
lour than of any other. 

In thcfe Defcriptions I have been the more 
particular, becaufe it is not impoffible but that 
Mifcrofcopes may at length be improved to the 
difcovery of the Particles of Bodies on which 
their Colours depend, if they are not already in 
fome meafure arrived to that degree of per- 
fedion. For if thofe Inftruments are or can be 
fo far improved as with fufficient diflindtnefs 
to reprefent Objedls five or fix hundred times 
bigger than at a Foot diftance they appear to 
our naked Eyes, I fliould hope that we might 
be able to difcover fome of the greatefi; of thofe 
Corpufcles. And by one that would magnify 
three or four thoufand times perhaps they might 
all be difcover'd, but thofe which produce 
blacknefs. In the mean while I fee nothing ma- 
terial in this Difcourfe that may rationally be 
doubted of, excepting this Pofition : That tran- 
fparent Corpufcles of the fame thicknefs and 
denfity with a Plate, do exhibit the fame Co- 
lour. And this I would have underftood not 
without fome Latitude,, as well becaufe thofe 
Corpufcles may be of irregular Figures, and 
many Rays muft be obliquely incident on them, 
and fo have a fliorter way through them than 
the length of their DiameterSj as becaufe the 

flraitnels 



B O O K II. 237 

ftraknefs of the Medium put in on all fides 
within fuch Corpufcles may a little alter its Mo- 
tions or other qualities on which the Reflexion 
depends. But yet I cannot much fufped: the 
laft , becaule I have obferved of fome fmall 
Plates of Mufcovy Glafs which were of an even 
thicknefs, that through a Microfcope they have 
appeared of the fame Colour at their edges and 
corners where the included Medium was ter- 
minated, which they appeared of in other pla- 
ces. However it will add much to our Satif^ 
fadion, if thofe Corpufcles can be difcover'd 
with Microfcopes ; which if we fhall at length 
attain to, I fear it will be the utmofl improve- 
ment of this Senfe. For it feems impoflible to 
fee the more fecret and noble Works of Nature 
within the Corpufcles by reafon of their tranfpa- 
rency. 

Prop. VIII. 

^he Cmife of Refcxion is not the impinging of 
Light on thefolid or impervious parts of Bodies^ 
as is commonly believed. 

np HIS will appear by the following Confi- 
-°- derations. Firft, That in the paflage of 
Light out of Glafs into Air there is a Reflexion 
as ftrong as in its palTage out of Air into Glafs, 
or rather a little ftronger, and by many degrees 
ilronger than in its pallage out of Glafs into Wa- 
ter. And it feems not probable that Air {hould 
have more flrongly refleding parts than Waf^r 
or Glafs. But if that ihould poflibly be fuppo- 
fed, yet it will avail nothing j for the Reflexion 



238 O P T I C K S. ' 

is as flrong or ftronger when the Air is drawn 
away from the Glafs, ( fuppofe by the Air-Pump 
invented by Otto Gueriet^ and improved and made 
ufeful by Mr. Boyle) as when it is adjacent to it. 
Secondly, If Light in its pafTage out of Glafs 
into Air be inqident more obUquely than at an 
Angle of 40 or 4 1 Degrees it is wholly refleded, 
if lefs obliquely it is in great meafure tranfmit- 
ted. Now it is not to be imagined that Light at 
one degree of obliquity fhould meet with Pores 
enough in the Air to tranfmit the greater part of 
it, and at another degree of obliquity fliould 
meet with nothing but parts to refled: it wholly, 
efpecially coniidering that in its palTage out of 
Air into Glafs, how oblique foever be its Inci- 
dence, it finds Pores enough in the Glafs to tranf- 
mit a great part of it. If any Man fuppofe that 
it is not refledled by the Air, but by the outmofl 
fuperficial parts of the Glafs, tliere is itill the 
fame dithculty: Befides, that fuch a Suppofition 
is unintelligible, and will alfo appear to be falfe 
by applying Water behind fome part of the Glafs 
inllead of Air. For fo in a convenient obliquity 
of the Rays, fuppofe of 45 or 46 Degrees, at 
which they are all refleded where the Air is adja- 
cent to the Glafs, they Ihall be in great meafure 
tranfmitted where the Water is adjacent to it; 
which argues, that their Reflexion or Tranfmiffi- 
on depends on the conilitution of the Air and 
W^ater behind the Glafs, and not on the ftriking 
of the Rays upon the parts of the Glafs. Third- 
ly, If the Colours made by a Prifm placed at 
the entrance of a Beam of Light into a darken'd 
Room te lucceffively call: on a fecond Prifm 

placed 



BOOK II. 239 

placed at a greater diftance from the former, 
in luch manner that they are all alike incident 
upon it, the fecond Prifm may be lo inclined to 
the incident Rays, that thole which are of a 
blue Colour fliall be all refleded by it, and yet 
thofe of a red Colour pretty copioufly tranlmit- 
ted. Now if the Reflexion be caufed by the 
parts of Air or Glafs, I would ask, why at the 
fame Obliquity of Incidence tiie blue fliould 
wholly impinge on thofe parts, fo as to be all 
reflected, and yet the red find Pores enough 
to be in a great meafure tranfmitted. Fourth- 
ly, Where two Glaffes touch one another, there 
is no fejifible Reflexion, as was declared in the 
iirft Obfervation; and yet I fee no feafon why 
the Rays fhould not impinge on the parts of 
Glafs, as much when contiguous to other Glafs 
as when contiguous to Air. Fifthly, When 
the top of a Water-Bubble (in the 17th Obfer- 
vation, ) by the continual fubflding and exha- 
ling of the Water grew very thin, there Vv^as 
fuch a little and almofl infenfible quantity of 
Light reflected from it, that it appeared in- 
tenfly black; whereas round about that black 
Spot, where the Water was thicker, -the Refle- 
xion was fo ftrong as to make the Water feem 
very white. Nor is it only at the leaft thick- 
nefs of thin Plates or Bubbles, that there is no 
manifeft Reflexion, but at many other thick- 
neffes continually greater and greater. For in 
the 15th Obfervation the Rays of the fame Co- 
lour were by turns tranfmitted at one thicknefs, 
and refledied at another thicknefs, for an in- 
determinate number of Succeflions. And yet 
I in 



2/,o , O P T I C K S. 

in the Superficies of the thinned Body, where 
it is of any one thicknefs, there are as many 
parts for the Rays to impinge on, as where it 
is of any other thicknefs. Sixthly, If Reflexion 
were caufed by the parts of reflecting Bodies, 
it would be impoilible for thin Plates or Bub- . 
bles, at one and the fame place, to refled; the 
Rays of one Colour, and tranfmit thofe of ano- 
ther, as they do according to the 13 th and 15 th 
Obfervations. For it is not to be imagined 
that at one place the Rays which, for infliance, 
exhibit a blue Colour, fliould have the fortune 
to dalh upon the parts, and thofe which exhi- 
bit a red to hit upon the Pores of the Body 5 
and tfien at another place, where the Body is 
either -a little thicker, or a little thinner, that 
on the contrary the blue fhould hit upon its 
pores, and the red upon its parts. Laftly, Were 
the Rays of Light refleded by impinging on 
the folid parts of Bodies, their Reflexions from 
polifh'd Bodies could not be fo regular as they 
are. For in polifliing Glafs with Sand, Putty, or 
Tripoly, it is not to be imagined that thofe 
Subftances can, by grating and fretting the Glafs, 
bring all its leafl: Particles to- an accurate Polifh; 
fo that all their Surfaces fliall be truly plain or 
truly fpherical, and look all the fame way, fo 
as together to compofe one even Surface. The 
fmaller the Particles of thofe Subftances are, 
the fmalier will be the Scratches by which they 
continually fret and wear away the Glafs until 
it be polifli'd j but be they never fo fmall they 
can wear away the Glafs no otherwife than by 
grating and fcratching it, and breaking the 
3 Protu-. 



BOOK 11. 241 

Protuberances; and therefore polifli it no o- 
therwife than by bringing its roughnefs to a ve- 
ry fine Grain, lb that the Scratches and Fret- 
tings of the Surface become too fmall to be 
vifible. And therefore if Light were refled:ed 
by impinging upon the folid parts of the Giafs, 
it would be fcatter'd as much by the moll po- 
lilh'd Glafs as by the rougheft. So then it re- 
anains a Problem, how Glafs poliili'd by fretting 
Subftances can refled; Light lb regularly as it 
does. And this Problem is fcarce otherwife to 
be folved, than by faying, that the Reflexion of 
a Ray is etfe(5ted, not by a lingle point of the 
reflecting Body, but by Ibme power of the Bo- 
dy which is evenly diffufed all over its Surface, 
and by which it a6ls upon the Ray without im- 
mediate Contad:. For that the parts of Bodies 
do a(fl upon Light at a diftance Ihall be Ihewn 
hereafter. 

Now if Light be refled:ed, not by impinging 
on the folid parts of Bodies, but by fome other 
principle j it's probable that as many of its Rays 
as impinge on the folid parts of Bodies are not 
refleded but ftifled and loll in the Bodies. For 
otherwife we mull allow two forts of Refle- 
xions. Should all the Rays be refledled which, , 
impinge on the internal parts of clear Water or 
Cryllal, thofe Subftances would rather have a 
cloudy Colour than a clear Tranfparency. To 
make Bodies look black, it's necefiary that ma- 
ny Rays be llopp'd, retained, and loft in them ; 
and it feems not probable that any Rays can be 
llopp'd and ftifled in them which do not im- 
pinge on their parts. 

R And 



a+2 O P T I C K S. 

And heilce we may underftand that Bodies 
are much more rare and porous^, than is com- 
monly believed. Water is nineteen times light- 
er, and by confequence nineteen times rarer 
than Gold ; and Gold is fo rare as very readily 
and vv^ithout the leafl oppofition to tranfmit the 
magnetick Effluvia, and eafily to admit Quick- 
filver into its Pores, and to let Water pafs 
through it. For a concave Sphere of Gold fil- 
led with Water, and folder'd up, has, upon pref- 
fmg the Sphere with great force, let the Water 
fqueeze through it, and ftand all over its out- 
fide in multitudes of fmall Drops, like Dew, 
without burfting or cracking the Body of the 
Gold, as I have been inform'd by an Eye-wit- 
nefs. From all which we may conclude, that 
Gold has more Pores than folid parts, and by 
confequence that Water has above forty times 
more Pores than Parts. And he that fhall find 
out an Hypothefls, by which Water may be fo 
rare, and yet not be capable of compreffion by 
force, may doubtlefs by the fapie Hypothefis 
make Gold, and Water, and all other Bodies, as 
much rarer as he pleafesj fo that Light may 
find a ready pafTage through tranfparent Sub- 
ftances. 

The Magnet ads upon Iron through all denfe 
Bodies not magnetick nor red hot,' without a- 
ny diminution of its Virtue ; as for inftance, 
through Gold, Silver, Lead, Glafs, Water. 
The gravitating Power of the Sun is tranfmit- 
ted through the vafl Bodies of the Planets with- 
out any diminution, fo as to ad; upon all their 
parts to their very centers with the fame Force 

and 



B O O K II. 243 

and according to the fame Laws, as if the part 
upon which it ads were not furrounded with 
the Body of the Planet. .The Rays of Light, 
whether they be very fmall Bodies . projeded, 
or only Motion or Force propagated, are mo- 
ved in right Lines ; and whenever a Ray of 
Light is by any Obftacle turned out of its rcdi- 
linear way, it will never return into the fame 
redilinear way, unlefs perhaps by very great ac- 
cident. And yet Light is tranfniittcd through 
pellucid folid Bodies in right Lines to very .great 
diftances. How Bodies can have a futikient 
quantity of Pores for producing thefe EtfcAs is 
very difficult to conceive, but perhaps not al- 
together impolTible. For the Colours of Bodies 
arife from the Magnitudes of the Particles winch 
refled them, as was explained above. Now if 
we conceive thefe Particles of Bodks to be fo 
difpofcd amongll themfelves, that the Intervals 
or empty Spaceb between them may be equal in 
magnitude to them all j and that tne£e i^arii- 
cles may be compufed of other Particles nmch 
fmaller, which have as much empty Space be- 
tween them as equals all the Magnitudes of 
thefe fmaller Particles: And that in like man- 
ner theie fmaller Particles are again compufed 
of others much fmaller, all which together are 
equal to all the Pores or empty Spaces between 
them; and fo on perpetually till \ou come to 
fond Particles, fuch 2.\ have no Pores or empty 
Spaces within them : And if in any grofs Lody 
there be, for inftance, three fuch degrees of 
Particles, the leaft of which are folid ; this Bo- 
dy will have feven times more Pores than folid 

R 2 Parts. 



244 O P T I C K S. 

Parts. But if there be four fuch degrees of 
Particles, the leaft of which are folid, the Bo- 
dy will have fifteen times more Pores than folid 
Parts. If there be five degrees, the Body will 
have one and thirty times more Pores than folid 
Parts. If fix degrees, the Body will have fixty 
and three times more Pores than folid Farts. And 
fo on perpetually. And there are other ways of 
conceiving how Bodies may be exceeding porous. 
But what is really their inward Frame is not yet 
known to us. 

Prop. IX. 

Bodies refeB and refradf Light by o?ie and the 
fame power, ^varioiijly exercijed in 'various- Cir- 
cumjiances. 

THIS appears by feveral Confiderations. 
Firft, Becaufe when Light goes out of 
Glafs into Air, as obliquely as it can pofiibly 
do. If its Incidence be made ftill more oblique, 
it becomes totally refledted. For the power of 
the Glafs after it has refracfled the Light as ob- 
liquely as is poflible, if the Incidence be ftill 
made more oblique, becomes too firong to let 
any of its Rays go through, and by confequence 
caufes total Reflexions. Secondly , Becaufe 
Light is alternately reflected and tranfmitted 
by thin Plates of Glafs for many Succeflions, 
accordingly as the thicknefs of the Plate increa- 
fes in an arithmetical Progreflion. For here 
the thicknefs of the Glafs determines whether 
that Power by which Glafs ad:s upon Light 
ihall caufe it to be rcfle(5ted, or fufier it to be 

tranf- 



BOOK 11. 



245 



tranfmitted. And, Thirdly, becaufe thofe Sur- 
faces of tranfparent Bodies which have the great- 
eft refradling power, refled the greateft quan- 
tity of Light, as was fliewn in the fir'll Propofi- 
tion. 

Prop. X. 

If Light be fwifter in Bodies 'than in Vacuo, in 
the proportion of the Sines which 7ncafure the 
RefraElion of the Bodies, the Forres of the 
Bodies to refcB and refrafl Light, are very 
nearly proportional to the denfities of the fame 
Bodies ; excepting that unBuous a?id fulphureous 
Bodies refraSt more than others of this fame den- 

LE T AB reprefent the refrading plane Sur- 
face of any Body, and IC a Ray incident 
very obliquely upon the Body in C, fo that the 




Angle ACI may be Infinitely little, and let CR 
be the refracfled Ray. From a given Point B 
perpendicular to the refradling Surface ered: B R 
meeting with the refrading Ray C R in R, and 
if C R reprefent the Motion of the refraded 
Ray, and this Motion be diftinguifh'd into two 
Motions CB and BR, whereof C B is paral- 

R 3 lei 



246 O P T I C K S. 

lei to the refracting Plane, and BR perpendi- 
cular, to it: CB fhall reprefent the Motion ^o.f 
the incident Ray, and B R the Motion genera- 
ted by the Reiradtion, as Opticians have of late 
explain'd. 

Now if any Body or Thing, in moving through 
any Space of a given breadth terminated on 
both fides by two parallel Planes, be urged for- 
ward in all parts of that Space by Forces tend- 
ing direftly forwards towards the laft Plane, and 
before its Incidence on the firil Plane, had no 
Motion towards it, -or but an infinitely little 
one J and if tlie Forces in all parts of that Space, 
between the Planes, be at equal diftances from 
the Planes equal to one another, but at feveral 
diftances be bigger or lefs in any given Propor- 
tion, the Motion generated by the Forces in 
the whole pafiage of the Body or thing through 
that Space fliall be in a fubduplicate Proportion 
of the Forces, as Mathematicians will eafily 
underftand. And therefore, if the Space of adti- 
vity of the refrafting Superficies of the Body 
be confider'd as fuch a Space, the Motion of 
the Ray generated by the refracting Force of 
the Body, during its pafiage through that Space, 
that is, the Motion B R, muft be in fubdupli- 
cate Proportion of that refracting Force. I fay 
therefore, that the Square of the Line B R, and 
by confequence the refracting Force of the Bo- 
dy, is very nearly as the denfity of the fame Bo- 
dy. For this will appear by the following Ta- 
ble, wherein the Proportion of the Sines which 
meafure the Refracftions of feveral Bodies, the 
Square of B R, fuppofing C B an unite, the Den- 

fities 



BOOK II. 247 

fities of the Bodies eftimated by their Specifick 
Gravities, and their Refradtive Power in refpea 
of their Denfities are fet down in feveral Co- 
lumns. 





The P report 


ion 1 The Square 


Theden- 


The re- 




of the %i 


ncs of B R, 


ffy and 


fiaSliz'e 




of Incidt 


nee 


to which 


fpccifick 


Pcicer 


The refrafting Bo- 


and Refra- 


the refra- 


gravi- 


of the 


dies. 


ftion of yel- 


Slingforce 


ty of 


Bod^ i n 




lovj Light 




of the Bo- 


thi Bo- 


refpeH 








dy is pro- 


dy. 


of its 








portionate 




denfity . 


APieudo-Top.-.zius, 










being a natural, 












pellucid, brittle, 


23 to 


H 


I '699 


4*27 


3979 


hairy Stone, of a 












yellow Colour. 












Air. 


3201 to 3 


200 


o''ooo62 5 


0'00I2 


5208 


Glafs of Antimony. 


17 to. 


9 


2*568 


5'28 


4864 


A Selenitis. 


61 to 


41 


I '2 1 3 


2*252 


5386 


Glafs vulgar. 


31 to 


20 


I '4025 


2'58 


543^ 


Cryibl 0*" the Rock. 


25 to 


16 


1^445 


2*65 


5450 


Jfl.lnd Cryftal. 


5 to 


3 


i'778 


2*72 


6536 


Sal GemmDC. 


17 to 


II 


i'388 


2*143 


6477 


Alume. 


35 to 


24 


1*1267 


1*714 


6570 


Borax. 


22 to 


»5 


I'lSii 


1*714 


67.6 


Niter. 


32 to 


21 


i'345 


i'9 


7079 


Dantzick Vitriol. 


303 to 


200 


1*295 


1*715 


755 » 


Oil of Vitriol. 


10 to 


7 


1*041 


>'7 


6124 


Rain Water. 


529 to 


396 


0*7845 


i' 


7845 


Gum Arabick. 


31 to 


21 


1*179 


i'37S 


8574 


Spirit of Wine well 
reftified. 


100 to 


73 


0*8765 


0*866 


10121 


Camphire. 


3 to 


2 


1*25 


0*996 


12551 


Oil Olive. 


22 to 


15 


1*1511 


0*913 


12607 


Linfeed Oil. 


40 to 


27 


1*1948 


0*932 


12819 


SpiritofTurpcntipe. 


25 to 


17 


1*1626 


0*874 


13222 


Amber. 


14 to 


9 


1*42 


1*04 


13654 


A Diamond. 


1 00 -to 


41 l4'949 


3*4 


i4556__ 



The Refradibn of the Air in this Table is de- 
termin'd by that of the Atmofphere obferved 

R 4 by 



248 O P T I C K S. 

by Aftronomers. For, if Light pafs through many 
refradling Subftances or Mediums gradually denfer 
and denfer, and terminated with parallel Surfaces, 
the Sum of all the Refradions will be equal to 
the iingle Refraction which it would have fuirer'd 
in paffing immediately out of the firft Medium 
into the lafl. And this holds true, though the 
Number of the refradling Subftances be increafed 
to Infinity, and the Diftances from one another 
as much decreafed, fo that the Light may be 
refraded in every Point of its Paflage, and by 
continual Refradions bent into a Curve-Line. 
And therefore the whole Refradlion of Light 
in paffing through the Atmofphere from the 
higheft and rareft Part thereof down to the loweft 
and denfeil Part, mufl be equal to the Re- 
fradion which it would fuffer in paffing at 
like Obliquity out of a Vacuum immediately 
into Air oi equal Denfity with that in the loweft 
Part of the Atmofphere. 

Now, although a Pfeudo-Topaz, a Selenitis, 
Rock Cryftal, Ifland Cryftal, Vulgar Glafs 
(that is. Sand melted together) 'and Glafs of 
Antimony, which are terreftrial ftony alcalizate 
Concretes, and Air which probably arifes from 
ftich Subftances by Fermentation, be Subftances 
very differing from one another in Denfity, yet 
by this Table, they have their refradive Powers 
almoft in the fame Proportion to one another 
as their Denfities are, excepting that the Re- 
fradion of that ftrange Subftance, Ifland Cryftal 
is a little bigger than the reft. And parti- 
cularly Air, which is 3500 Times rarer than 
the Pfeudo-Topaz, and 4.400 Times rarer than 
a Glafs 



BOOK IL 249 

Glafs of Antimony; and 2000 Times rarer than 
the Seleniti8, Glafs vulgar, or Cryflal of the 
Rock, has notwithftanding its rarity the fame re- 
fradive Power in refped: of its Denfity which 
thofe very denfe Subftances have in refped of 
theirs, excepting fo far as thofe differ from one 
another. 

Again, the Refraction of Camphire, Oil Olive, 
Linfeed Oil, Spirit of Turpentine and Amber, 
which are fat fulphureous unduous Bodies, and 
a Diamond, which probably is an unduous Sub- 
ftance coagulated, have their refradive Powers in 
Proportion to one another as their Denlities with- 
out any confiderable Variation. But the re- 
fradive Powers of thefe undluous Subftances are 
two or three Times greater in refpedt of their 
Denfities than the refradive Powers of the former 
5ubftances in refped of theirs. 

Water has a refradive Power in a middle de- 
gree between thofe two forts of Subflances, 
and probably is of a middle nature. For out 
of it grow all vegetable and animal Subftances, 
which confift as well of fulphureous fat and in- 
flamable Parts, as of earthy lean and alcalizate 
ones. 

Salts and Vitriols have refradive Powers in a 
middle degree between thofe of earthy Subflances 
and Water, and accordingly are compofed of 
thofe two forts of Subflances. For by dill illation 
and redification of their Spirits *a great Part of 
them goes into Water, and a great Part remains 
behind in the form of a dry fix'd Earth capable 
of Vitrification. 

Spirit 



250 O P T I C K S. 

Spirit of Wine has a refradiv^e Power in a 
middle degree between thofe of Water and oily 
Subftances, and accordingly feems to be compo- 
fed of both, united by Fern^.entation; the Water, 
by means of fome faline Spirits with which 'tis 
impregnated, dillolving the Oil, and volatizing 
it by the Ad;ion. For Spirit of Wine is inflama- 
blc by means of its oily Parts, and being diftilled 
often from Salt of Tartar,, grow by every diftil- 
lation more and more aqueous and phlegma- 
tick. And Chymiils obferve, that Vegetables 
(as Lavender, Rue, Marjoram, (^f. ) diftilled ^^r 
fe^ before fermentation yield Oils without any 
burning Spirits, but after fermentation yield ar- 
dent Spirits without Oils : W^hich fliews, that 
their Oil is by fermentation converted into Spi- 
rit. They find alfo, that if Oils be poured in a 
fmall quantity upon fermentating Vegetables, 
they diftil over after fermentation in the form 
of Spirits* 

So then, by the foregoing Table, all Bodies 
feem to have their retradive Powers propor- 
tional to their Denfities, (or vei'y nearly;) ex- 
cepting fo far as they partake more or lefs of 
iulphureous oily Particles, and thereby have their 
refradiive Power made greater or lefs. Whence 
it feems rational to attribute the refrad-ive Power 
of all Bodies chiefly, if not wholly, to the ful- 
phureous Parts with which they abound. For 
it's probable that all Bodies aJDOund more or lefs 
with Sulphurs. And as Light congregated by a 
Burning-glafs ads moft upon fulphureous Bo- 
dies, to turn them into Fire and Flame ; fo, 
fince all Adion is mutual. Sulphurs ought to a6t 

moft 



BOOK II. 251 

moil upon Light. For that the action between 
Light and Bodies is mutual, may appear from 
this Confideration ; That the denfeil Bodies 
which rtfrad: and reflect Light moft Wrongly, 
grow hotteft in the Summer Sun, by the adtion 
of the refradcd or refied:ed Light. 

I have hitherto explain'd the power of Bo- 
dies to reflect and refradt, and (liew'd, that thin 
tranfparent Plates, Fibres, and Particles, do, ac- 
cording to their feveral thickneifes and dcnli- 
ties, refled: feveral forts of Ravs, and thereby 
appear of feveral Colours; and by confecjuence 
that nothing more is requifitc for producing all 
the Colours of natural Bodies, than the feveral 
fizes and denfities of their tranfparent Particles. 
But whence it is that thefe Plates, Fibres, and 
Particles, do, according to their feveral thick- 
nelTes and denfities, refledt feveral forts of kays, 
I have not yet explain'd. To give fome infight 
into this matter, and make way for underftand- 
ing the next part of this Book, I fhall conclude 
this part with a few more Proportions. Thofe 
which preceded refpeft the nature of Bodies, 
thefe the nature of Light : For both mufl be 
underftood, before the reafon of their Adlions 
upon one another can be known. And becaufe 
the laft Propofition depended upon the velocity 
of Light, I will begin with a Propofition of that 
kind. 



Prop. 



252 O P T I C K S. 

Prop. XL 

Light is propagated from luminous Bodies in 
time, and Jpends about feven or eight Mi- 
nutes of an Hour in paffing from the Sun to the 
Earth, 

'l ^ HIS was (obferved firfl by Roemer, and 
-*- then by others, by means of the Eclipfes of 
the Satellites of Jupiter. For thefe Eclipfes, 
when the Earth is between the Sun and Jupiter, 
happen about itvtn. or eight Minutes fooner 
than they ought to do by the Tables, and when 
the Earth is beyond the Sun they happen about 
feven or eight Minutes later than they ought to 
do; the reafon bemg, that the Light of the 
Satellites has farther to go in the latter cafe 
than* in the former by the Diameter of 
the Earth's OrbiL Some inequalities of time 
may arife from the Excentricities of the Orbs of 
the Satellites ; but thofe cannot anfwer in all the 
Satellites, and at all times to the Poiition and 
Diftance of the Earth from the Sun. The mean 
motions of Jupiter s Satellites is alfo fwifter in 
his defcent from his Aphelium to his Perihelium, 
than in his afcent in the other half of his Orb. 
But this inequality ha^ no refpcd: to the pofition 
of the Earth, and in the three interior Satellites 
5s infenfible, as I find by computation from the 
Theory of their Gravity. 



Prop. 



BOOK IL 



Prop. XII. 



253 



Every Ray of Light in its pajfagc through any 
refraBing Surface is put into a certain trajijicnt 
Conjlitution or State ^ which in the progrefs 
of the Ray returns, at equal Intervals^ and 
difpofes the Ray at every return to be eafily 
tranfmitted through ' the next refraSfitjg Sur- 
face, and betiveen the returns to be eafdy refieSied 
by it. 

TH I S is manifeil by the 5th, 9th, 12th, 
and 15th jObfervations. For by thofe Ob- 
fervations it appears , that one and the fame 
fort of Rays at equal Angles of Incidence on a- 
ny thin tranfparent Plate, is alternately refledled 
and tranfmitted for many Succeffions according- 
ly as the thicknefs of the Plate increafes in 
arithmetical Progreffion of the Numbers, o, 

I, 2, 3, 4, 5, 6, 7, 8, ^c. fo that if the firft 
Reflexion ( that which makes the firfl: or inner- 
moft of the Rings of Colours there defcribed ) 
be made at the thicknefs i, the Rays fliall be 
tranfmitted at the thicknelTes o, 2, 4, 6, 8, lo, 

12, ^c. and thereby make the central Spot and 
Rings of Light, which appear by tranfmillion, 
and be refledied at the thicknefs i, 3, ^, 7, o, 

I I, ^c. and thereby make the Rings which 
appear by Reflexion. And- this alternate Re*- 
flexion and TranfmilTion, as I gather by the 24th 
Obfervation, continues for above an hundred 
viciflitudes, and by the Obfervations in the next 
part of this Book, for many thoufands, being 
propagated from one Surface of a Glafs Plate to 

the 



254 O P T I C K S. 

the other, though the thicknefs of the Plate be 
a quarter of an Inch or above : So that this al- 
ternation feems to be propagated from every 
refrading Surface to all diflances w^ithout end or 
limitation. 

This alternate Reflexion and Refradtion de- 
pends on both the Surfaces of every thin Plate, 
becaufe it depends on their diflance. By tlie 
21 ft Obfervation, if either Surface of a thin 
Pjate of Miifcovy Glafs be wetted, the Colours 
caufed by the alternate Reflexion and Refraction 
grow faint, and therefore it depends on them 
both. 

It is therefore performed at the fecond Surface; 
for if it were perform'd at the firft, before the 
Rays arrive at the fecond, it would not depend 
on the fecond. 

It is alfo influenced by fome action or difpo- 
fition, propagated from the firft to the fecond, 
becaufe other wife at the fecond it v^ould not 
depend on the firft. And this adion or difpo- 
fition, in its propagation, intermits and returns 
by equal Intervals, becaufe in all its progrefs it 
inclines the Ray at one diftance from the- firft 
Surface to be reflefted by the fecond, at ano- 
ther to be tranfmitted by it, and that by equal 
Intervals for innumerable viciflitudes. And be- 
caufe the Ray is difpofed to Reflexion at the 
diliances i, 3, 5, 7, 9, ^c. and to Tranfmiflion 
at the diftances o, 2, 4, 6, 8, 10, Gfr. (for its 
tranfmillion through the firft Surface, is at the 
diftance o, and it is tranfmitted tiirough both 
together, if their diftance be infinitely little or 
much lefs than i ) the difpofition to be tranf- 
I mit.e4 



BOOK 11. 255 

mitted at the diftances 2, 4, 6, 8, 10, &c. is to be 
accounted a return of the lame difpofition which 
the Ray firft had at the diftance o, that is at its 
tranfmiffion through the firft refradling Surface. 
All which is the thing I would prove. 

What kind of adion or difpofition this is; 
Whether it confifts in a. circulating or a vibra- 
ting motion of -the Ray, or of the Medium, or 
fomething elfe, I do not here enquire. Thofe 
that are averfe from alTenting to any new Dif- 
coveries, but fuch as they can- explain by an Hy- 
pothecs, may for the prefent fuppofe, that as 
Stones by falling upon Water put the Watef in- 
to an undulating Motion, and all Bodies by 
percufTion excite vibrations in the Air; fo the 
Rays of Light, by impinging on any refracting 
or reflecfting Surface , excite vibrations in the 
refrafting or refiecfting Medium or Subftance, 
and by exciting them agitate the folid parts of 
the refrad:ing or reflecting Body, and by agita- 
ting them caufe the Body to grow warm or 
hot; that the vibrations thus excited are pro- 
pagated in the refradting or reflecfting Medium 
or Subftance, much after tlie manner that vibra- 
tions are propagated in the Air for caufing 
Sound, and move fafter than the Rays fo as to 
overtake thenij and that when any Ray is in 
that part of the vibration which confpires with 
its Motion, it eafily breaks through a refrading 
Surface, but when it is in the contrary part of 
the vibration which impedes its Motion, it is 
eafily reflected ; and, by confequence, that e- 
very Ray is fucceftively difpofed to be eafily re- 
flected, or eafliy tranfmitted, by every vibration 

which 



256 O P T I C K S. 

which overtakes it. But whether this Hypothe- 
lis be true or falfe I do not here conlider. I con- 
tent my felf with the bare Difcovery, that the 
Rays of Light are by fome caufe or other alter- 
nately difpofed to be refled:ed or refraded for 
many viciffitudes. 

DEFINITION. 

I'he returns of the difpofition of any Ray to be 
refeBed I will call its Fits of eafy Reflexion, 
and thofe of its difpoftion to be tranfmitted its 
Fits of eafy Tranfmiffion, and the [pace it 
pa[fes between every return and the next re- 
tunty the Interval of its Fits. 

Prop. XIII, 

'The reafon why the Surfaces of all thick tranf- 
farent Bodies refledi part of the Light inci^ 
dent on thein^ and refraSi the reji ^ isy that 
fome Rays at their Incidence are in Fits of eafy 
Reflexion^ a7id others in Fits of eafy Tranf- 
mifjion. 

np HIS may be gather'd from the 24th Ob- 
-*- fervation, where the Light reflected by 
thin Plates of Kv: and Glafs, which to the naked 
Eye appear'd evenly white all over the Plate, did 
through a Prifm appear waved with many Suc- 
ceffions of Light and Darknefs made by alter- 
nate Fits of eafy Reflexion and eafy Tranfmiffi- 
on, the Prifm fevering and difl:inguifliing the 
Waves of which the white refledled Light was 
compofed, as was explain' d above. 

And 



BOOK II; 2^7 

And hence Light is in Fits of cafy Reflexion 
and eafy Tranfmiflion, before its Incidence on 
tranfparent Bodies. And probably it is put in- 
to fuch Fits at its firfl emilTion from luminous 
Bodies, and continues in them during all its pro- 
grefs. For thefe Fits are of a lafting naturcj as 
will appear by the next part of this Book. 

In this Proportion I fuppofe the tranfparent 
Bodies to be thick j becaufc if the thicknefs of 
the Body be much lefs than the Interval of the 
Fits of eafy Reflexion and Tranfmitiion of the 
Rays, the Body lofeth its refleclling power. For 
if the Rays, which at their entering into the' 
Body are put into Fits of eafy Tranfmiflion, ar- 
tive at the farthefl Surface of the Body before 
they be out of thofe Fits, they muil: be tranfmit- 
ted. And this is the reafon why Bubbles' of 
Water lofe their refledling power when they 
grow very thin ; and why all opake Bodies, when 
reduced into very fmall parts, become tranfpa^ 
rent. 

Prop. XIV. 

'Thofe Surfaces cf tranfparent Bodies^ which if the 
Ray be in a Fit of 'Refratlicn do rfra6i it vicf: 
fli-ongly^ if the Ray be in a Fit of Rcfiexion do 
refeB it 7nofi eafdy. 

FO R we fhewed above, in Frop. 8. that thai 
caufe of Reflexion is not the impinging of 
Light on the folid impervious parts of Bodies^ 
but fome other power by which thofe folid 
parts ad; on Light at a diilance. We fhewed 
alio in Frop, 9. that Bodies refled: and refrad: 

S Lighc 



258 O P T I C K S. 

Light by one and the fame power, varloufly ex- 
ercifed in various circumftances; and in Prop. i. 
that the moft ftrongly refracting Surfaces refledt 
the moft Light: All which compared together 
evince and ratify both this and the laft Propo- 
rtion. 

Prop. XV. 

In any one and the fame fort of Rays, emerging in 
any Angle out of any refraSling Surface into one 
and the fame Medium, the hitervalaf the fol- 
lowing Fits of eafy Refexion and 'T^ranfmifjion 
are either accurately or very nearly, as the ReB- 
angle of the Secaiit of the Angle of RefraSlion, 
and of the Secant of another Angle, whofe Sine 
is the firfi of 106 arithmetical mean Rroporti- 
onals, between the Sines of Incidence and Refra- 
Bion, counted from the Si?2e of RefraBion. 

T^ H I S is manifefl by the 7th and 19th Obfcr- 
••■" vations. 



Prop. 



B O O K n. 259 

Prop. XVI. 

Lt fever al forts of Rays e-merging in equal Anglci. 
out of any refradiing Surface into the fame Me^ 
dium^ the Litervals of the foiio'wing hits of eafy 
'Reflexion and eafy T'ranfniJJion are either accu- 
rately, or very nearly, as the Cube-Roots of the 
Squares of the lengths of a Chord, which fownd 
the Notes in an Eight, fol, la, fa, fol, la, mi, 
fa, fol, ivith all their imter mediate degrees an- 
fuoering to the Colours of thofe Rays, accordtfg to 
the Analogy defcrihed in the feventh Experiment 
of the fecond Part of theflrft Book. 

np H I S is manifeft by the 13th and 14th Ob- 
■*■ fervations. 

Prop. XVII. 

Jf Rays of any fort pafs perpendicularly ifito feve^ 
ral Mediums, the hitcrvcls of the Fits cf eafy 
Reflexion and l^ranfmiflion in any one Medium, 
are to thofe Intervals in any other, as the Sine of 
Incidence to the Sine of RefraBion, wlmi the 
Rays pafs out of the flrfl of thofe ti^o Mediums 
into the fecond. 

T^ H I S is manifeft by the loth Obferva- 
-^ tion. 



S 2 Prop, 



26o O P T I C K S. 

Prop. XVIII. 

If the Rays nvhich paint the Colour in the Confine 
of yellow and orange pafs perpejidicularly out of 
any Medium into Air, the Intervals of their Fits 

of eafy Reflexion are the th part of an Inch, 

And of the fa?ne length are the Intervals of their 
Fits of ' eafy I^ranfmifjion, 

^ I ^ H I S is manifeft by the 6th Obfervation. 
-*" From thefe Propofitions it is eafy to col- 
led: the Intervals of the Fits of eafy Reflexion 
and eafy Tranfmiffion of any fort of Rays refra- 
ined in any Angle into any Medium j and thence 
to know, whether the Rays fhall be reflected, or 
tranfmitted at their fubfequent Incidence upon 
any other pellucid Medium. Which thing, be- 
ing ufeful for underflanding the next part of this 
Book, was here to be fet down. And for the 
fame reafon I add the two following Propofi- 
tions. 



Prop, 



BOOK II. 261 

Prop. XIX. 

If any fort of Rays faUi7ig on the polite Surface 
of any pellucid Medium be refeBed back^ the Fits 
of eafy Refexion^ which they have at the point of 
Refexion, fall fill continue to return j a?jd the 
Returns fiall be at diftances from the point of 
Refexicn in the arithmetical prcgrejfon of the 
'Numbers 7.^ 4, 6, 8, 10, 12, &c. and between 
thefe Fits the Rays pall be in Fits of eafy 7'rafif 
mijjion. 

"P O R fiRce the Fits of eafy Reflexion and 
•*- Qafy TranfmilTion are of a returning na- 
ture, there is no reafoa why thefe Fits, which 
continued till the Ray arrived at the reflecting 
Medium, and there inclined the Ray to Refle- 
xion, ihould there ceafe. And if the Ray at the 
point of Reflexion was in a Fit of eafy Reflexion, 
the progreflion of the diftances of thefe Fits 
from that point mufl: begin from o, and fo be of 
the Numbers o, 2, 4, 6, 8, &c. And therefore 
the progreffion of the dillances of the interme- 
diate Fits of eafy Tranfmiflion, reckon'd from 
the fame point, mufl be in the progreflion of 
the odd Numbers i, 3, 5, 7, 9, ^c. contrary 
to what happens when the Fits are propagated 
from points of Refradion. 



S3 Prop, 



262 O P T I C K S. 

Prop. XX. 

^he Intervals of the Fits of eafy Reflexion and, 
eafy T'ranfmifjion^ propagated from points of 
KeHexion into afiy Medium^ are equal to the 
Intervals of the like Fits^ which the fame Rays 
would ba-vey if refraBed into the fame Medium 
in Angles of Rejraciion equal to their Angles of 
Reflexion, 

'P O R when Light is refleded by the fecond 
■"- Surface of thin Plates, it goes out after- 
wards fieely at the firft Surface to make the 
Rin^s of Colours which appear by Reflexion j 
and, by the freedom of its egrefs, makes the 
Colours of thefe Rings more vivid and ftrong 
than thofe which appear on the other fide of 
the Plates by the tranfmitted Light. The re- 
fieded Rays are therefore in Fits of eafy Tranf- 
miffion at their egrefs; v/hich would not always 
happen, if the Intervals of the Fits within the 
Plate after Reflexion were not equal, both in 
kngth and number, to their Intervals before it. 
And this confirms alfo the proportions fet down 
in the former Propofition. For if the Rays 
both in going in and out at the firfh Surface be 
in Fits of eafy Tranfmiffion, and the Intervals 
and Numbers of thofe Fits between the firft 
and fecond Surface, before and after Reflexion, 
be equal, the diftances of the Fits of eafy 
Tranfmiflion from either Surface, muft be in 
the fame prpgreffion after Reflexion as before ; 
that is, from the firft Surface which tranfmit- 
ted them, in the progreffion of the even Num-. 

bers 



B O O K IL 263 

bers o, 2, 4, 6, 8, (^c. and from the fecond 
which refledled them, in that of the odd Num- 
bers I, 3, 5, 7, &c. But thefe two Propofi- 
tions will become much more evident by the 
Obfervations in the following part of this 
Book. 




S4 



THE 




THE 

SECOND BOOK 



O F 



OPTICKS 



PART IV. 



Qbfervations concerning the Reflexions and 
Colour^ of thick tranfparent polij^d 
Platzs. 






HERE Is no Glafs or Speculum how 
well foever polifliedjbut, befides the 
Light which it refradts or refledls re-, 
gularlyj fcatters every way irregularly 
a faint Light, by means of which the 
polifh'd Surface, v/hen illuminated in a dark room 

by 




BOOK II. 265 

by a beam of the Sun's Light, may be eafily feen 
in all pofitions of the Eye. There are certain 
Phaenomena of this fcatter'd Light, which when 
I firft obferved them, feem'd very flrange and 
furprizing to me. My Obfervations were as fol- 
lows. 

Obf. I. The Sun fhining into ray darkened 
Chamber through a hole one third of an Inch 
wide, riet the intromitted beam of Light fall 
perpendicularly upon a Glafs Speculum ground 
concave on one fide and convex on the other, 
to a Sphere of five Feet and eleven Inches Ra- 
dius, and Quick-filver'd over on the convex 
fide. And holding a white opake Chart, or a 
Quire of Paper at the center of the Spheres to 
which the Speculum was ground, that is, at the 
diftance of about live Feet and eleven Inches 
from the Speculum, in fuch manner, that the 
beam ©f Light might pafs through a little hole 
made in the middle of the Chart to the Specu- 
lum, and thence be reflected back to the fime 
hole: I obferved upon the Chart four or five 
concentric Irifes or Rings of Colours, like Rain- 
bows, encorapaffing the hole much after the 
manner that thofe, which in the fourth and fol- 
lowing Obfervations of the firft part of this third 
Book appear'd between the Objedl-glaiTes, en- 
compafled the black Spot, but yet larger and 
fainter than thofe. Thefe Rings as they grew 
larger and larger became diluter and fainter, fo 
that the fifth was fcarce vifible. Yet fome- 
times, when the Sun llione very clear, there 
appear'd faint Lineaments of a fixth and fe- 
vgnth. If the diftance of the Chart from the 

S,pecu-» 



266 O P T I C K S. 

Speculum was much greater or much lefs than 
that of fix Feet, the Rings became dilute and 
vaniQi'd. And if the diftance of the Speculum 
from the Window was much greater than that 
of fix Feet, the refledied beam of Light would 
be fo broad at the diftance of fix Feet . from the 
Speculum where the Rings appear'd, as to ob- 
fcure one or two of the innermoft Rings. And 
therefore I ufually placed the Speculum at a- 
bout fix Feet from the Window j fo that its 
Focus might there fall in with the center of its 
concavity at the Rings upon the Chart. And 
this Pofiiure is always to be underfi:ood in the 
following Obfervations where no other is ex- 
prefs'd. 

Obf. 2. The Colours of thefe Rain-bows fuc- 
ceeded one another from the center outwards, 
in the fame form and order with thofe which 
were made in the ninth Obfervation of the firft 
Part of this Book by Light not refledled, but 
tranfmitted through the two Objedi-glafiTes. For, 
firfi:, there was in their common center a white 
round Spot of faint Light, fomething broader 
than the refleded beam of Light, which beam 
fometimes fell upon the middle of the Spot, and 
fometimes by a little inclination of the Specu- 
lum receded from the middle, and left the Spot 
white to the center. 

This white Spot was immediately encompaf- 
fed with a dark grey or rufleti and that dark grey 
with the Colours of the firfi: Iris; which Colours 
on the infide next the dark grey were a little 
violet and indigo, and next to that a blue, which 
on the outfide grew pale, and then fucceeded a 

little 



BOOK 11. 267 

little greenifh yellow, and after that a brighter 
yellow, and then on the outward edge of the 
Iris a red which on the outfide inclined to pur- 
ple. 

This Iris was immediately encompaffed with a 
fecond, whofe Colours were in order from the in- 
fide outwards, purple, blue, green, "yellow, light 
red, a red mix'd with purple. 

Then immediately foUow'd the Colours of the 
third Iris, which were in order outwards a green 
inclining to purple, a good green, and a red more 
bright than that of the former Iris. 

The fourth and fifth Iris feem'd of a bluifli 
green within, and red without, but fo faintly 
that it was difficult to difcern the Colours. 

Obf. 3. Meafuring the Diameters of thefe 
Rings upon the Chart as accurately as I could, 
I found them alfo in the fame proportion to 
one another with the Rings made by Light tranf- 
mitted through the two Objed-glafies. For 
the Diameters of the four iirfl of the brjf^ht 
Rings meafured between the brightefl parts of 
their Orbits, at the diftance of fix Feet from the 
Speculum were 144, 2I, 2— 3^ Inches, whofe 
Squares are in arithmetical progreffion of the 
numbers i, 2, 3, 4. If the white circular Spot 
in the middle be reckon'd amongfl the Rings, 
and its central Light, where it fsems to be n:oil 
luminous, be put equipollent to an infinitely 
little Ring ; the Squares of the Diameters of the 
Rings will be in the progrefiion o, i, 2, 3, 4, 
&c. I meafured alfo the Diameters of the dark 
Circles between thefe luminous ones, and found 
their Squares in the progreflion of the num- 
bers 



268 O P T I C K S.^ 

bers T, It, 2^, 3^, '&c. the Diameters of the 
firft four at the diftance of fix Feetsfrom the 
Speculum, being i.?^, 2tV, 2t, 3tt Iiiches. If 
the diftance of the Chart from the Speculum 
was increafed or diminilhed, the Diameters of 
the Circles were increafed or diminifhed pro- 
portionally. 

Obf. ^. By the analogy between thefe Rings 
and thofe defcribed in the Obfervations of the 
firft Part of this Book, I fufpedted that there 
were many more of them which fpread into 
one another, and by interfering mix'd their Co- 
lours, and diluted one another fo that they could 
not be feen apart. I viewed them therefore 
through a Prifm, as I did thofe in the 24th Ob- 
fervation of the firft Part of this Book. And 
when the Prifm was fo placed as by refradling 
the Light of their mix'd Colours to feparate 
them, and diftinguilh the Rings from one ano- 
ther, as it did thofe in that Obfervation, I could 
then fee them diftind:er than before, and eafily 
number eight or nine of them, and fometimes 
twelve or thirteen. And had not their Light 
been fo very faint, I queftion not but that I might 
have feen many more. 

Ohf. 5. Placing a Prifm at the Window to re- 
fradl the intromitted beam of Light, and caft 
the oblong Speftrum of Colours on the Specu- 
lum : I covered the Speculum with a black Pa- 
per which had in the middle of it a hole to let 
any one of the Colours pafs through to the Spe- 
culum, whilft the reft were intercepted by 
the Paper. And now I found Rings of that Co- 
lour only which fell upon the Speculum. If 

the 



BOOK II. 269 

the Speculum was illuminated with red, the 
Rings were totally red with dark Intervals, if 
with blue they were totally blue, and fo of the 
other Colours. And when they v/ere illumi- 
nated wi'th any one Colour, the Squares of their 
Diameters meafured between their moil lumi- 
nous Parts, were in the arithmetical Progreilion 
of the Numbers, o, i, 2, 3, 4, and the Squares 
of the Diameters of their dark Intervals in the 
Progreffion of the intermediate Numbers j, It, 
2f, 33. But if the Colour was varied, they va- 
ried their Magnitude. In the red they were lar- 
geft, in the indigo and violet leaft, and in the 
intermediate Colours yellow, green, and blue, 
they were of feveral intermediate Bigneffes an- 
fwering to the Colour, that is, greater in yel- 
low than ia green, and greater in green than in 
blue. And iicnce I knew, that when the Spe- 
culum was illuminated with white Light, the 
red and yellow on the outlide of the Rings were 
produced by the hoA refrangible Rays, and the 
blue and violet by the moir refrangible, and that 
the Colours of each Ring fpread into the Co- 
lours of the neighbouring Rings on either fide, 
after the manner explain'd in the firft and fe- 
cond Part of this Book, and by mixing diluted 
one another fo tliat they could not be diflin- 
guifli'd, unlefs near the Center where they were 
leaft mix'd. For in this Obfervation I could 
fee the Rings more diftindly, and to a greater 
Number than before, being able in the yellow 
Light to number eight or nine of them, be- 
iides a faint ihadow of a tenth. To fatisfy my 
felf how much th^ Colours of the feveral Rings 

fpread 



270 O P T I C K S. 

fpread Into one another, I meafured the Dia- 
meters of the fecond and third Rings, and found 
them when made by the Confine of the red and 
orange to? be to the fame Diameters when made 
by the Confine of blue and indigo, as 9 to 8, 
or thereabouts. For it was hard to determine 
this Proportion accurately. Alfo the Circles 
made fuccefiively by the red, yellow, and green, 
differ'd more from one another than thofe made 
fuccefTively by the green, blue, and indigo. For 
the Circle made by the violet was too dark to 
be feen. To carry on the Computation, let us 
therefore fuppofe that the Differences of the 
Diameters of the Circles made by the outmoft 
red, the Confine of red and orange, the Confine 
of orange and yellow, the Confine of yellow 
and green, the Confine of green and blue, the 
Confine of blue and indigo, the Confine of in- 
digo and violet, and outmoft violet, are in pro- 
portion as the Differences of the Lengths of a 
Monochord which found the Tones in an Eight j 
jbl, la^ fa, Jol, la, mi, fa, fol, , that is, as the 
Numbers ir, tV, tV, t'-, tV, tV> ■^' ^"d if the 
Diameter of the Circle made by the Confine of 
red and orange be 9 A, and that of the Circle 
made by the Confine of blue and indigo be 8 A 
as above ; their difference 9 A — 8 A will be 
to the difference of the Diameters of the Cir- 
cles made by the outmoft red, and by the Con- 
fine of red and orange, as tV -1- tt A- rV -^ tV ^o \, 
that is as tV to \, or 8 to 3, and to the diffe- 
rence of the Circles m.ade by the outmoft vio- 
let, and by the Confine of blue and indigo, as 

TT 4- TT -1- tV 4- vT to rr 4- iV, that is, as -iy to tV> 

or 



BOOK IL 271 

or as 16 to 5. And therefore thefe differences 
will be g A and /g A. Add the firft to 9 A and 
fubdud the lafi: from 8 A, and you will have the 
Diameters of the Circles made by the leafl and 

moft refrangible Rays ''i. A and -^ A. Thefe di- 
ameters are therefore to one another as 75 to 
61^ or 50 to 41, and their Squares as 2500 to 
168 1, that is, as 3 to 2 very nearly. Which 
proportion differs not much from the proportion 
of the Diameters of the Circles made by the 
outmoft red and outm-oft violet, in the 13 th Ob- 
fervation of the firft part of this Book. 

Ol?f. 6. Placing my Eye where thefe Rings 
appear'd plaineft, I faw the Speculum tinged all 
over with Waves of Colours, (red, yellov/, green, 
blue J ) like thofe which in the Obfervations of 
the firft part of this Book appeared between 
the Obje(3:-glaffes, and upon Bubbles of Water, 
but much largei". And after the manner of thofe, 
they were of various magnitudes in various Po- 
litions of the Eye, fwellin-^ and ihrinking as I 
moved my Eye this way and that way. They 
were formed like Arcs of ccnccntrick Circles, as 
thofe were 5 and v/hen my Eye was over againft 
the center of the concavity of tho Speculum, (that 
is, 5 Feet and 10 Inches diftant from the Specu- 
lum,) their common center was in a right Line 
with that center of concavity, and with the 
hole in the Window. But m other poftures of 
my Eye their center had other pofitions. They 
appear'd by the Light of tlie Clouds propagated 
to the Speculum through the hole in the Win- 
dow J and when the Sun {hone through that 

2 hole 



272 O P T I C K S. 

hole upon the Speculum, his Light upon it was 
of the Colour of the Ring whereon it fell, but by 
its fplendor obfcured the Rings made by the Light 
of the Clouds, unlefs when the Speculum was 
removed to' a great diftance from the Window, 
fo that his Light upon it might be broad and faint. 
By varying the polition of my Eye, and moving 
it nearer to or farther from the direct beam of the 
Sun's Light, the Colour of the Sun's refleded 
Light conflantly varied upon the Speculum, as it 
did upon my Eye, the fame Colour always ap- 
pearing to a By-ftander upon my Eye which to 
me appear'd upon the Speculum. And thence I 
knew that the Rings of Colours upon the Chart 
were made by thefe refledled Colours, propagated 
thither from the Speculum in feveral Angles, and 
that their produdion depended not upon the ter- 
mination of Light and Shadow. 

Obf. J. By the Analogy of all thefe Pheno- 
mena with thofe of the like Rings of Colours 
defcribed in the f rft part of this Book, it feem- 
ed to me that thefe Colours were produced by 
this thick Plate of Glafs, much after the manner 
that thofe were produced by very thin Plates. 
For, upon trial, I found that if the Quick-fil- 
ver were rubb'd off from the backfide of the 
Speculum, the Glafs alone would caufe the 
fame Rings of Colours, but much more faint 
than before j and therefore the Phaenomenon 
depends not upon the Quick-lilver, unlefs fo far 
as the Quick-hlver by increaiing the Reflexion 
of the backfide of the Glafs increafes the Light 
of the Rings of Colours. I found alfo that a 
Speculum of Metal without Glafs made fome 

Years 



BOOK II. 273 

Years fince for optical ufes, and very well 
wrought, produced none of thofe Rings j and 
thence I underfbood that thefe Rings arifc not 
from one fpecular Surface alone, but d'epend 
upon the two Surfaces of the Plate of Glafs 
whereof the Speculum was made, and upon the 
thicknefs of the Glafs between them. For 
as in the 7th and 19th Obfervations of the firft 
part of this Book a "thin Plate of Air, Water, 
or Glafs of an even thicknefs appeared of one 
Colour when the Rays were perpendicular to 
it, of another v/hen they were a little oblique, 
of another v/hen more oblique, of another when 
ftill more oblique, and fo on y fo here, in the 
lixth Obfervation, the Light which emerged 
out of the Glafs in feveral Obliquities,- made tlie 
Glafs appear of feveral Colours, and being pro- 
pagated in thofe Obliquities to the Chart, tiierc 
painted Rings of thofe Colours. And as the 
reafon why a thin Plate appeared of feveral Co- 
lours in feveral Obliquities of the Rays, v/as, 
that the Rays of one and the fame fort are re- 
fleded by the thin Plate at one obliquity and 
tranfmitted at another, and thofe of other forts 
tranfmitted where thefe are refleded, and re- 
flected where thefe are tranfmitted : So the 
reafon why .the thick Plate of Glafs whereof 
the Speculum was made did appear of various 
Colours in various Obliquities, and in thofe 
Obliquities propagated thofe , Colours to the 
Chart, was, that the Rays of one and the 
fame fort did at one Obliquity emerge out 
of the Glafs, at another did not emerge, but 
were refleded back towards the Quick-filver 

T . by 



t74 O P T I C K S. 

by the hither Surface of the Glafs, and according- 
ly as the Obliquity became greater and greater, 
emerged and were refiedted alternately for ma- 
ny Succeffignsj and that in one and the fame 
Obliquity the Rays of one fort were refled:ed, 
and thofe of another tranfmitted. This is ma- 
nifeft by the fifth Obfervation of this part of this 
Book. For in that Obfervation, when the Spe- 
culum was illuminated by any one of the prif- 
matick Colours, that Light made many Rings 
of the fame Colour upon the Chart with dark 
Intervals, and therefore at its emergence out of 
the Speculum was alternately tranfmitted and 
not tranfmitted from the Speculum to the Chart 
for many SuccefTions, according to the various 
Obliquities of its Emergence. And when the 
Colour caft on the Speculum by the Prifm was 
varied, the Rings became of the Colour cafl on 
it, and varied their bignefs with their Colour, 
and therefore the Light was now alternately 
tranfmitted and not tranfmitted from the Spe- 
culum to the Chart at other Obliquitiss than 
before. It feemed to me therefore that thefe 
Rings were of one and the fame original with 
thofe of thin Plates, but yet with this difference, 
that thofe of thin Plates are made by the alter- 
nate Reflexions and Tranfmiffions of the Rays 
at the fecond Surface of the Plate, after one paf- 
fage through itj but here the Rays go twice 
through the Plate before they are alternately re- 
ileded and tranfmitted. Firft, they go through 
it from the firfi: Surface to the Quick-filver, and 
then return through it from the Quick-filver 
to the firil Surface, and there are either tranf- 
mitted 



BOOK II. 275 

micted to the Chart or refledled back to the 
Quick-filver, accordingly as they are in their 
Fits of eafy Reflexion or Tranfmiffion when 
they arrive at that Surface. For the Intervals 
of the Fits of the Rays which fall perpendicu- 
larly on the Speculum,, and are reiledled back 
in the fame perpendicular Lines, by rcafon" of 
the equality of tbefe Angles and Lines, are of 
the fame length and number within the Glafs 
after Reflexion as before, by the 19th Propofl- 
tion of the third part of this Book. And there- 
fore fince all the Rays that enter through the 
iirll: Surface are in their Fits of eafy Tranfmif- 
fion at their entrance, and as many of thefe as 
are refledted by the fecond are in their Fits of 
eafy Reflexion there, all thefe mufl: be again in 
their Fits of eafy Tranfmiffion at their return 
to the firil, and by confequence there go Out 
of the Glafs to the Chart, and form upon it the 
white Spot of Light in the center of the Rings. 
For the reafon holds good in all forts of Rays, 
and therefore all forts mufl go out promifcu- 
oufly to that Spot, and by their mixture " caufe 
it to be white. But the Intervals of the Fits of 
thofe Rays which are reflected more obliquely 
than they enter, mull: be greater after Reflexion 
than before, by the 15th and 20th Propcfitlons. 
And thence it may happen that the Rays at their 
return to the firli Surface, may in certain Ob- 
liquities be in Fits of eafy Reflexion, and return 
back to the Qu]ck-f:!ver, and in other interme- 
diate Obliquities be again in Fits of eafy Tranf- 
miffion, and fo go out to the Chart, and paint 
on it the Rings of Colours about the white Spot. 

T 2 And 



276 O P T I C K S. 

And becaufe the Intervals of the Fits at equal 
obliquities are greater and fewer in the lefs re- 
franf^ible Rays, and lefs and more numerous in 
rhe more refrangible, therefore the lefs refrangi- 
ble at equal obliquities fhall make fewer Rings 
than the more refrangible, and the Rings made 
by thofe iliall be larger than the like number of 
Rings made by thefej that is, the red Rings 
fhali be larger than the yellow, the yellow than 
the green, the green than the blue, and the blue 
than the violet, as they were really found to be 
in the fifth Obfervation. And therefore the firll 
Ring of all Colours encompaffing the white 
Spot of Light lliall be red without any violet 
within, and yellow, and green, and blue in the 
middle, as it was found in the fecond Obferva- 
tion ; and thefe Colours in the fecond Ring, and 
thofe that follow, fliall be more expanded, till 
they fpread into one another, and blend one an- 
other by interfering. 

Thefe feem to be the reafons of thefe Rings 
in general j and this put me upoi;i obferving the 
thicknefs of the Glals, and confidering whether 
the dimenfions and proportions of the Rings may 
be truly derived from it by computation. 

Obf. 8. I meafured therefore the thicknefs of 
this concavo-convex Plate of Glafs, and found it 
every where \ of an Inch precifely. Now, by 
the fixth Obfervation of the firft Part of this 
Book, a thin Plate of Air tranfmits the brighteft 
Light of the firft Ring, that is, the bright yel- 
low, when its thicknefs is the g-^ th part of an 

Inchi and by the tenth Obfervation of the fame 

Part, 



BOOK IT. 277 

Parr, a thin Plate of Glafs trLinfmits the fame 
Light of" the farrie Ring, when its diicknefs k 
lefs in proportion of tb.e Sine of Refrad:ion to 
the Sine of Incidence, that is, when its thick- 

nefs is the ,-- 1 '";;;;;; th or - ' — th part of an Inch, 
1^13000 137545 ^ 

fappofing the Sines are as 1 1 to 17. And it this 
thickncfs be doubled, it tranfmits the fame bright 
Light of thefecond Ring; if trippled, it tranf- 
mits that "of tlie third, and fo on; the bright 
yellow Light in all thefe cafes being in its Fits 
of Tranfmiiiion. And therefore if its thickncfs 
be multiplied 34386 times, fo as to become J of 
an Inch, it tranfmits the fame bright Liglit of 
the 34386th Ring. Suppofe this be the bright 
yellow Light tranfmitted perpendicularly from 
the refled-ing convex lide of the Glafs through 
the concave fide to the white Spot in the cen- 
ter of the Rings of Colours on the Chart: And 
by a Rule in the 7th and igvh Obfervations in 
the firft Part of this Book, and by the J5ch and 
20th Propofitions of the third Part of this Book, 
if the Rays be made oblique to the Glafs, the 
thickncfs of the Glafs requilite to tranfmit the 
fame bright Light of the fame Ring in any ob- 
liquity, is to this fliickncfs of; of an Inch, as the- 
Secant of a certain Angle to the Radius, the 
Sine of which. Angle is the firfl of an hundred 
and fiX arithmetical Means between the Sines 
of Incidence and Rcfrartion, counted from the 
Sine of Incidence when the Refrac^liion is made 
out of any plated Body into any Medium en- 
compafTmg it ; that isj in this cafe, out of Glafs 
into Air. Now if the thicknefs of the Glafs be 

T 3 increafed 



278 O P T I C K S. 

increafed by degrees, fo as to bear to its firft 
thicknefs, (viz. that of a quarter of an Inch,)' 
the Proportions which 34386 .(the number of 
Fits of the perpendicular Rays in ^oing through 
the Glafs tov/ards the white Spot in the center 
of the Rings,) hath to 34385, 34384, 34383, and 
34382, (the' numbers of the Fits of the oblique 
Rays in going through the Glafs towards the 
firft, fecond, third, and fourth Rings of Co- 
lours, ) and if the firfl thicknefs be divided in- 
to 1 00000000 equal parts, the increafed thick- 
nefies will be 1 00002908, 1 00005 8 1 6, 1 00008725, 
and 100011633, and the Angles of which thefe 
thicknelTes are Secants will be 26' 13", 37' 5", 
45' 6", and 52' 26", the Radius being looooooooj 
and die Sines of thefe Angjjes are 762, 1079, 
1321, and 1525, and the proportional Sines of 
Refradion 1 172, 1659, 203 1, and 2345, the Ra- 
dius being 1 00000. For fmce the Sines of In- 
cidence out of Glafs into Air are to the Sines 
of Refraiftion as 11 to 17, and to the above- 
mentioned Secants as 1 1 to the iirft of 106 arith- 
metical Means betVv^een 11 and 17, that is, as; 

1 1 to II —>, thofe Secants will be to the Sines 
106' 

of Refradion as 11 -j^ to 17, and by this Ana- 
logy will give thefe Sines. So then, if the ob- 
liquities of the Rays to the concave Surface of 
the Glafs be fuch that the Sines of their Refra- 
dion in paiTing out of the Glafs through that 
Surface into the Air be 1172, 1659, 2031, 2345, 
the bright Light of the 34386th Ring fhall e- 
jnerge at the thickneffes of the Glafs, which are 

2 to 



BOOK II. 279 

to 5 of aninch as 34386 to 34385,.34384, 34383, 
34382, refpedively. And therefore, if the thick- 
nefs in all thefe Cafes T3e 5 of an Inch (as it is in 
the Glafs of which the Speculum was made) 
the bright Light of the 34385th Ring fhall e- 
merge where the Sine of Refracftion is 1 172, 
and that of the 34384th, 34383th, and 34382th 
Ring where the Sine is 1659, 2031, and 2345 
refpedtively. And in thefc Angles of Refra- 
ction the Light of thefe Rings fliall be propaga- 
ted from the Speculum to the Chart, and there 
paint Rings about the white central round Spot 
of Light which we faid was the Light of thp 
34386th Ring. And the Semidiameters of thefe 
Rings fhall fubtend the Angles of Refraction 
made at the Concave-Surface of the Speculum, 
and by confequence their Diameters flrjll be to 
the diftance of the Chart from the Speculum as 
thofe Sines of Refraction doubled are to the 
Radius, that is, as 1172, 1659, 2031, and 2345, 
doubled are to 1 00000. And therefore, if the 
diftance of the Chart from the Concave-Surface 
of the Speculum be fix Feet ( as it was in the 
third of thefe Obfervations ) the Diameters of 
the Rings of this bright yellov/ Light upon the 
Chart fhall be i'688, 2*389, 2*925, 3*375 Inches: 
For thefe Diameters are to fix Feet, as the above- 
mention'd Sines doubled are to the Radius. 
Now, thefe Diameters of the bright yellow 
Rings, thus found by Computation are the 
very fame with thofe found in the third of thefe 
Obfervations by meafuring them, viz. with 
I IS, 2g, 2ii, and 3g Inches,, and therefore the 
1 heory of deriving thefe Rings from the thick- 

T 4 nsfs 



28o O P T I C K S. 

nefs of the Plate of Glafs"* of which the Specu- 
.lurii was made, and from the Obliquity of the 
emerging P.ays agrees with the Obfervation. In 
this Computation 1 have equalled the Diameters 
of the bright Rings made by Light of all Co- 
lours, to the Diameters of the Rings made by 
the bright yellow. For this yellow makes the 
brighteft Part of the Rings of all Colours. If 
you defire theDiameters of the Rings made by the 
Light of any other unmix'd Colour, you may 
find them readily by putting them to the Diame- 
ters of the bright yellow ones in a fubduplicate 
Proportion of the Intervals of the Fits of the 
Rays of thofe Colours when equally inclined to 
the refrading or reflecting Surflice which caufed 
thofe Fits, that is, by putting the Diameters of 
the Rings made by the Rays in the Extremities 
and Limits of the feven Colours, red, orange, 
yellow, green, blue, indigo, violet, proportio- 
nal to the Cube-roots of the Numbers, i, |, ^, J, 
|, 55 -^5 ly which exprefs the Lengths of a Mono- 
chord founding the Notes in an Lighth: For 
by this m.eans the Diameters of the Rings of 
thefe Colours will be found pretty nearly in 
the fame Proportion to one another, which 
they ought to have by the fifth of thefe Obferva- 
tions. 

And thus I fatisfy'd my felf, that thefe Rings 
were of the fame Kind and Original with thofe 
of thin Plates, and by confequenxe that the Fits 
or alternate Difpofitions of the Rays to be 
refleded and tranfmirted are propagated to 
great diftances from every refleding and re- 
frading Surface. But yet to put the mat- 
ter 



BOO K II, 281 

ter out of doubt, I added the following Obfer- 
vation. 

Obf. 9. If ^thefe Rings thus depend on the 
thicknels of the Plate of Glafs, ' their Diameters 
at equal diilances from feveral Speculums made 
of iuch CDncavo-convex Plates of Glafs as are 
ground on the fame Sphere, ought to be recipro- 
cally in a fubduplicate Proportion of the thick- 
neffes of the Plates of Glafs. And if this Pro- 
portion be found true by experience it will amount 
to a demonftratlon that thefe Rings (like thofe 
formed in thin Plates) do depend on the thick- 
nefs of the Glafs. I procured therefore ano- 
ther concavo-convex Plate of Glafs ground on 
both lides to the fame Sphere with the former 
Plate. Its thicknefs was l^ Parts of an Inch ; 
and the Diameters of the three hYi\. bright Rings 
meafured between the brightell Parts of their 
Orbits at the diftance of fix Feet from the 
Glafs were 3. 4^-. 5J. Inches. Now, the thick- 
nefs of the other Glafs being \ of an Inch v/as 
to the thicknefs of this Glafs as ? to 4 that is 
as 31 to 10, or 310000000 to icooooooo, and 
the Roots of thefe Numbers are 1 7607 and loooo, 
and in the Proportion of the iirlt of thefe Roots 
to the fecond are the Diameters of the brip-ht 
Rings made in this Obfervation by the tliinner 
Glafs, 3. 4fi. 57, to the Diam.eters of the fime 
Rings made in the tliird of thefe Obfervations" 
by the thicker Glafs i-.^. 2!. 2^k, that is, the Dia- 
meters of the Rings are reciprocally in a fubdu- 
plicate Proportion of the thickneffcs of the Plates 
of Glafs. 



282 O P T I C K S. 

So then in Plates of Glafs which are alike 
concave on one fide, and alike convex on the 
other fide, and alike quick-filver'd on the con- 
vex fides, and differ in nothing but ' their thick- 
nefs, the Diameters of the Rings are reciprocally 
in a fubduplicate Proportion of the thickneffes of 
the Plates. And this fhew^s fufticiently that the 
Rings depend on both the Surfaces of the Glafs, 
They depend on the convex Surface, becaufe they 
lare more luminous when that Surface is quick- 
filver'd over than when it is without Quick-filver. 
They depend alfo upon the concave Surface, be- 
caufe without that Surface a Speculum makes them 
not. They depend on both Surfaces, and on the 
difiiances between them, becaufe their bignefs is 
varied by varying only that diftance. And this 
dependance is of the fame kind with that which 
the Colours of thin Plates have on the difi:ance 
of the Surfaces of thofe Plates, becaufe the big- 
nefs of the Rings, and their Proportion to one 
another, and the variation of their bignefs arifing 
from the variation of the thicknefs of the Glafs, 
and the Orders of their Colours, is fuch as ought 
to refult from th© Propofitions in the end of the 
third Part of this Book, derived from the Phaeno- 
mena of the Colours of thin Plates fet down in 
the firfi: Part. 

There are yet other Phenomena of thefe Rings 
of Colours, but fuch as follow from the fame 
Propofitions, and therefore confirm both the 
Truth of thofe Propofitions, and the Analogy be^ 
tween thefe Rings and the Rings of Colours 
made by very thin Plates. I fhali fubjoin fome 
of them. 

ObJ\ 



BOOK II. 283 

Obf. 10. When the beam of the Sun's Light 
was refleded back from the Speculum not di- 
redly to the hole in the Window, but to a pLce 
a little diftant from it, the common center of 
that Spot, and of all the Rings of Colours fell 
in the middle way between the beam of the in- 
cident Light, and the beam of the refleded 
Light, and by confequence in the center of the 
fpherical concavity of the Speculum, whenever 
the Chart on which the Rings of Colours fell 
was placed at that center. And as the beam of 
refledfed Light by inclining the Speculum re- 
ceded more and more from the beam of inci- 
dent Light and from the common center of the 
colour'd Rings between them, thofe Rings grew 
bigger and bigger , and fo alfo did the white 
round Spot, and new Rings of Colours emer- 
ged fucceffively out of their common center, 
and the white Spot became a white Ring en- 
compaffing them 3 and the incident and reflected 
beams of Light always fell upon the oppofite 
parts of this white Ring, illuminating its Peri- 
meter like two mock Suns in the oppofite parts 
of an Iris. So then the Diameter of this Ring, 
meafured from the middle of its Light on one 
lide to the middle of its Light on the other fide, 
was always equal to the diftance between the 
middle of the incident beam of Light,'' and the 
middle of the refleded beam meafured at the 
Chart on which the Rings appeared: And the 
Rays which form'd this Ring were reflected by 
the Speculum in Angles equal to their Angles of 
Incidence, and by confequence to their Angles 
pf Refradion at their entrance into the Glafs, 

but 



284 O P T I C K S. 

but yet their Angles of Reflexion were not in 
the fame Planes with their Angles of Inci- 
dence. 

' Obf. 1 1. The Colours of the new Rings Were 
in a contrary order to thofe of the former, and 
arofe after this manner. • The white round Spot 
of Light in the middle of the Rings continued 
white to the center till the diftance of the inci- 
dent and refleded beams at the Chart was about 
8 parts of an Inch, and then it began to grow 
dark in the middle. And when that diftance was a- 
bout ItV of an Inch, the white Spot was become 
a Ring encompaffing a dark round Spot which in 
the middle inclined to violet and indigo. And 
the luminous Rings encompafling it were grown 
equal to thofe dark ones which in the four firft 
Obfervations encompafled them, that is to fay, 
the white Spot was grown a white Ring equal to 
the firft of thofe dark Rings, and the firft of 
thofe luminous Rings was now grown equal to 
the fecond of thofe dark ones, and the fe- 
cond of thofe luminous ones to the third of 
thofe dark ones, and fo on. For the Diameters 
of the luminous Rings were now itV, 2'V, 2j, 
3 iV, S^c. Inches. 

When the diftance between the incident and 
reflected beams of Light became a little big- 
ger, there emerged out of the middle of the 
dark Spot after the indigo a blue, and then out 
of that biue a pale green, and foon after a yel- 
low and red. And when the Colour at the 
center was brighteft, being between yellow and 
red, the bright Rings were grown equal to thofe 
Rings -which in the four firft Obfervations next 

encom- 



BOOK II. 285 

encompaiTed them; that is to fay, the white 
Spot in the middle of thofe Rings was now be- 
come a white Ring equal to the iirft of thofe 
bright Rings, and the firft of thofe bright ones 
was now become equal to the fecond of thofe, 
and fo on. For the Diameters of the white 
Ring, and of the other luminous Rings encom- 
paffing it, were now 1 44, 2|, 2|i, 3|., J^c. or 
thereabouts. 

When the diftance of the two beams of 
Light at the Chart was a little more increafed, 
there emerged out of the middle in order after 
the red, a purple, a blue, a green, a yellow, 
and a red inclining much to purple, and when 
the Colour was brighteft being between yellow 
and red, the former indigo, blue, green, yel- 
low and, red, were become an Iris or Ring of 
Colours equal to the firlt of thofe luminous 
Rings which appeared in the four firfh Obfer- 
vations, and the white Ring which was now 
become the fecond of the luminous Rings was 
grown equal to the fecond of thofe, and the 
lirft of thofe which was now become the third 
Ring was become equal to the third of thofe, 
and fo on. For their Diameters were Itx, 2g, 
2-rT, 3 1- Inches, the diftance of the two beams 
of Light, and the Diameter of the v/hite Ring 
being 2t Inches. 

When thefe two beams became more diflant 
there emerged out of the middle of the pur- 
plifh red, firft a darker round Spot, and then 
out of the middle of that Spot a brighter. And 
now the former Colours ( purple, blue, green, 
yellow, and purplilh red) were become a Ring 

equal 



286 O P T. I C K S. 

equal to the firft of the bright Rings mentioned 
in the four firfl Obfervations, and the Rings 
about this Ring were grown equal to the Rings 
about that refpedtively j the diftance between 
the two beams of Light and the Diameter of the 
white Ring ( which was now become the third 
Ring ) being about 3 Inches. 

The Colours of the Rings in the middle be- 
gan now to grow very dilute, and if the di- 
ftance between the two Beams was increafed 
half an Inch, or an Inch more, they vanifh'd 
whilfl the white Ring, with one or two of the 
Rings next it on either fide, continued ftill vi- 
able. But if the diftance of the two beams of 
Light was ftill more increafed, thefe alfo va- . 
nifhed: For the Light which coming from fe- 
veral parts of the hole in the Window fell up- 
on the Speculum in feveral Angles of Incidence, 
made Rings of feveral bigneffes, which diluted 
and blotted out one another, as I knew by inter- 
cepting fome part of that Light. For if I in- 
tercepted that part which was neareft to the 
Axis of the Speculum the Ring's would be lefs, 
if the other part which was remoteft from it 
they would be bigger. 

Obf. 12. When the Colours of the Prifm 
were caft fucceffively on the Speculum, that 
Ring which in the two laft Obfervations was 
white, was of the fame bignefs in all the Co- 
lours, but the Rings without it were greater in 
the green than in the blue, and ftill greater in 
the yellow, and greateft in the red. And, on the 
contrary, the Rings within that white Circle 
were lefs in the green than in the blue, and ftill 

lefs 



BOOK II. 287 

lefs in the yellow, and leaft in the red. For the 
Angles of Reflexion of thofe Rays which made 
this Ring, being equal to their Angles of Inci- 
dence, the Fits of every reflected Ray within 
the Glafs after Reflexion are equal in length 
and number to the Fits of the fame Ray with- 
in the Glafs before its Incidence on the refled:- 
ing Surface. And therefore flnce all the Rays 
of all forts at their entrance into the Glafs were 
in a Fit of Tranfmiffion, they were alfo in a Fit 
of Tranfmiflion at their returning to the fame 
Surface after Reflexion j and by confequence 
were tranfmitted, and went out to the white 
Ring on the Chart. This is the reafon why 
that Ring was of the fame bignefs in all the Co- 
lours, and why in a mixture of all it appears 
white. But in Rays which are reflefted in o- 
ther Angles, the Intervals of the Fits of the 
leaft refrangible being greateft, make the Rings 
of their Colour in their progrefs from this white 
Ring, either outwards or inwards, increafe or 
decreafe by the greateft fteps ; fo that the Rings 
of this Colour without are greateft, and within 
leaft. And this is the reafon why in the laft 
Obfervation, when the Speculum was illumina- 
ted with white Light, the exterior Rings made 
by all Colours appeared red without and blue 
within, and the interior blue without ^nd red 
within. 

Thefe. are the Pha?nomena of thick convexo- 
concave Plates of Glafs, which are every where 
of the fame thicknefs. There are yet other 
Phaenomena when thefe Plates are a little thick- 
er on one fide than on the other, and others 

when 



288 O P T I C K S. 

when the Plates are more or lefs concave than 
convex, or plano-convex, or double-convex. For 
in all thefe cafes the Plates make Rings of Co- 
lours, but after various manners; all which, fo 
far as I have yet obferved, follow from the Pro- 
pofitions in the end of the third part of this 
Book, and fo confpire to confirm the truth of 
thofe Propofitions. But the Phaenomeiia are 
too various, and the Calculations whereby they 
follow from thofe Proportions too intricate to 
be here profecuted. I content my felf with ha- 
ving profecuted this kind of Phaenomena fo far 
-as to difcover their Caufe, and by difcovering 
it to ratify the Propofitions in the third Part of 
this Book. 

Obf. 13. As Light reflecSled by a Lens quick- 
iilver'd on the backfide makes the Rings of Co- 
lours above defcribed, fo it ought to make the 
like Rings of Colours in pafling through a drop 
of Water. At the firft Reflexion of the Rays 
within the drop, fome Colours ought to be 
tranfmitted, as in the cafe of aj^ens, and others 
to be refie(^l:ed back to the Eye. For inftance, 
if the Diameter of a fmall drop or globule of 
"Water be about the 500th part of an Inch, fo 
that a red-making Ray in paffing through the 
middle of this globule has 250 Fits of eafy 
Tranlhiifiion within the globule, and that all 
the red-making Rays which are at a certain di- 
ftance from this middle Ray round about it 
have 249 Fits within the globule, and all the 
like Rays at a certain farther diftance found a- 
bout it have 248 Fits, and all thofe at a cer- 
tain farther diftance 247 Fits, and fo on; thefe 

concern- 



BOOK II. 2S9 

concentrick Cirdes of Rays after their tranf- 
miiTion, falling on a white Paper, will make 
concentrick Rings of red upon the Paper, fup- 
pofing the Light .which pafles through one An- 
gle globule, llrong enough to be fenlible. And, 
in like manner, the Rays of other Colours will 
make Rings of other Colours. Suppole now 
that in a fair Day the Sun ihines through a thin 
Cloud of fuch globules of Water or Hail, and 
that the globules are all of the fame bignefs; 
and the Sun feen through this Cloud fhall ap- 
pear encompaffed with the like concentrick 
Rings of Colours, and the Diameter of the firfl: 
Ring of red fliall be 7 1. Degrees, that of the fe- 
cond 10 i Degrees, that of the third 12 Degrees 
33 Minutes. And accordingly as the Globules 
of Water are bigger or lefs, the Rings lliall be 
lefs or bigger. This is the Theory, and Expe- 
rience anfwers it. For in 'jiuh; 1692, I faw by 
reflexion in a Veflel of ftagnating Water three 
Halos, Crowns, or Rings of Colours about the 
Sun, like three little Rain-bows, concentrick 
to his Body. The Colours of the firft or In- 
nermoft Crown were blue next the Sun, red 
without, and white in the middle between the 
blue and red. Thofe of the fecond Crown 
were purple and blue within, and pale red with- 
out, and green in the middle. And thofe of 
the third were pale blue within, and pale red 
without; thefs Crowns enclofed one another 
immediately , fo that their Colours proceeded 
in this continual order from the Sun outward: 
blue, white, red 3 purple, blue, green, pale 

U yello;v 



290 O P T I C K S. 

yellow and red j pale blue, paid red. The Di- 
ameter of the fecond Crown meafured from 
the middle of the yellow and red on one fide 
of the Sun, to the middle of the fame Colour 
on the other fide was gr Degrees, or therea- 
bouts. The Diameters of the firfl and third 
1 had not time to meafure, but that of the firfl 
feemed to be about five or fix Degrees, and 
that of the third about twelve. The like 
Crov/ns appear fometimes about the Moon; 
for in the beginning of the Year 1664, Fel?r, 
19th at Night, I faw two fuch Crowns about 
her. The Diameter of the firfi: or innermoft 
was about three Degrees, and that of the fe- 
cond about five Degrees and an half Next a- 
bout the Moon was a Circle of white, and next 
about that the inner Crown, which was of a 
bluifli green within next the white, and of a 
yellow and red without, and next about thefe 
Colours were blue and green on the infide of 
the outward Crown, and red on the outfide of 
it. At the fame time there appear'd a Halo a- 
bout 22 Degrees 35' diftant from the center of 
the Moon. It was elliptical, and its long Dia- 
meter was perpendicular to the Horizon, verg- 
ing belovv farthefk from the Moon. I am told 
that the Moon has fometimes three or more 
concentrick Crowns of Colours encompafiing 
one another next about her Body. The more 
equal the globules of Water or Ice are to one 
another, the more Crowns of Colours will ap- 
pear, and the Colours will be the more lively. 
The Halo at the diilance of 22t Degrees from 

the 



BOOK 



IL 291 

By its beino; oval 



the Moon is of another fort, 
and remoter from the Moon beiow than above, 
I conclude, that it v^cis made by Refradlion in 
fome fort of Hail or Snow floating in the Air in 
an horizontal pofture, the refra<5ting Angle being 
about 58 or 60 Degrees. 




U 2 



THE 



^ 


1 


©^ 


m 




i 


1 


>^ 



THE 



THIRD BOOK 



O F 



OPTICKS 



PART 1. 



Ohfervations concerning the Inflexions of 
the Rays of Lights and the Colours 
made thereby. 

RIMALDO has inform'd us, that 
if a beam of the Sun's Light be let in- 
to a dark Room through a very fmall 
hole, the Shadows of things in this 
Light will be larger than they ought to be if 
the Rays went on by the Bodies in ilrait Lines, 

and 




BOOK III. 293 

and 'that thefe Shadows have three parallel 
Fringes, Bands or Ranks of colour'd Light ad- 
jacent to them. Rut if the Hole be enlarged 
the Fringes grow broad and run into one ano- 
ther, fo that they cannot be diftinguifh'd. Thefe 
broad Shadows 'and Fringes have been reckon'd 
by fome to proceed from the ordinary refra6tion 
of the Air, but without due examination of the 
Matter. For the circumftances of the Phano- 
nienon, fo far as I have obferved them, are as 
follows. 

Obf. I. I made in a piece of Lead a fmall 
Hole with a Pin, whofe breadth was the 42d 
part of an Inch. For 2 1 of thofe Pins laid to- 
gether took up the breadth of half an Inch. 
Through this Hole I let into my darken'd 
Chamber a beam of the Sun's Light, and found 
that the Shadows of Hairs, Thred, Pins, Straws, 
and fuch like flender Subftances placed in this 
beam of Light, were confiderably broader than 
they ought to be, if the Rays of Light pa fled 
on by thefe Bodies in right Lines. And parti- 
cularly a Hair of a Man's Head, whofe breadth 
was but the 280th part of an Inch, being held in 
this Light, at the diftance of about twelve Feet 
from the Hole, did caft a Shadow which at the 
diftance of four Inches from the Hair was the 
fixtieth part of an Inch broad, that is, above " 
four times broader than the Hair, ' and at the di- 
ftance of two Feet from the Hair Vs^as about the 
eight and twentieth part of an Inch broad, that 
is, ten times broader than the Hair, and at the 
diftance of ten Feet was the eighth part of an 
Inch bsoad, that is 35 times broader, 

U 3 Nor 



294 O P T I C K S. 

Nor is it material whether the Hair be en- 
compaffed with Air, or with any other pellucid 
Subllance. For I wetted a polifli'd Plate of 
Glafs, and laid the Hair in the Water upon the 
Glafs, and. then laying another polifli'd Plate of 
Glafs upon it, fo that the Water* might fill up 
the fpace between the GlafTes, I held them in 
the aforefaid beam of Light, fo that the Light 
might pafs through them perpendicularly, and 
the Shadow of the Hair was at the fame di- 
flances as big as before. The Shadows of 
Scratches made in polifh'd Plates of Glafs were 
alfo much broader than they ought to be, and 
the Veins In polifh'd Plates of Glafs did alfo caft* 
the like broad Shadows. And therefore the 
great breadth of thefe Shadows proceeds from 
feme other caufe than the" Refraction of the 
Air. 

Let the Circle X [in Fig. i.] reprefent the 
middle of the Hair; ADG, BEH, CFI, 
three Rays pafTmg by one fide of the Hair at 
feveral diflances ; KNQ^LOR, MPS, three 
other Rays paffmg by the other fide of the Hair 
at the like diflancesj D, E, F, and N, O, P, the 
places where the Rays are bent in their paf- 
fage by the Hair j G, H, I, and Q^, S, the 
places where the Rays fall on a Paper GQ^ 
I S the breadth of the Shadow of the Hair cafl 
on the Paper, and TI, VS, two Rays paffing 
to the Points 1 and S without bending when 
the Hair is taken away. And it's manifefl that 
all the Light between thefe two Rays TI and 
VS is bent in paffmg by the Hair, and turned 
alide from the Shadow I S, becaufe if any part 

cf 



BOOK III. 295 

of this Light were not bent it would fall on the 
Paper within the Shadow, and there illuminaie 
the Paper, contrary to experience. And becaufe 
when the Paper is at a great diftance from the 
Hair, the Shadow is broad, and ■ therefore the 
Rays TI and VS are *at a great diftance from 
one another, it follows that the Hair ads unon 
the Rays of Light at a good diltance in their paf- 
fing by it. But the Action is frrongeft on the 
Rays which pafs by at leaft^ diflances, and 
grows weaker and weaker accordingly as the 
Rays pafs by at diftances greater and greater, as 
is reprefented in the Scheme : For thence it 
comes to pafs, that the Shadow of the Hair is 
much broader in proportion to the diflance of the 
Paper from the Hair, when the Paper is nearer 
the Hair, than when it is at a great diftance 
from it. 

0I?j:2. The Shadov/s of all Bodies (Metals, 
Stones, Glafs, Wood, Horn, Ice, &c. ) in this 
Light were border'd with three Parallel Fringes 
or Bands of coloured Light, whereof that which 
was contiguous to the Shadow was broadeft 
and moft luminous, and that which was remo- 
teft from it was narroweft, and fo faint, ^ as not 
eafily to be vifible. It v/as difficult to diftinguiili 
the Colours, unlefs when the Light fell very ob- 
liquely/upon a fmooth Pap:-r, or fome other 
fmooth white Body, fo as to make them appear 
much broader than they would otherwife do. 
And then the Colours were plainly vifible in 
this Order: The tirft or innermoft Fringe wViS 
violet and deep blue next the Shadow, and then 
light blue, green, and yellow in the middle, ai :d 

U 4 .r^^d 



2o6 O P T I C K S. 

red without. The fecond Fringe was almoft 
contiguous to the firft, and the third to the fe- 
cond, and both were blue within, and yellow and 
red without, but their Colc^rs were very faint, 
cfpecially thofe of the third. The Colours there- 
fore proceeded in this order from the Shadow ; 
violet, indigo, pale blue, green, yellow, red ; 
blue, yellow, red; pale blue, pale yellow and 
red. The Shadows made by Scratches and 
Bubbles in polifh'd Plates of Glafs were bor- 
der'd with the like Fringes of colour'd Light. 
And if Plates of Looking-glafs floop'd off near 
the edges with a Diamond-cut, be held in the 
fame beam of Light, the Light which paffes 
through the parallel Planes of the Glafs will be 
border'd with the like Fringes of Colours where 
thofe Planes meet with the Diamond-cut, and 
by this means there will fometimes appear four 
or five Fringes of Colours. Let AB, CD [in 
Vig. 2.] reprefent the parallel Planes of a Look- 
ing-glafs, and B D the Plane of the Diamond- 
cut, making at B a very obtufe Angle with the 
Plane AB. And let all the Light between the 
Rays ENI and FBM pafs diredly through the 
parallel Planes of the Glafs, and fall upon the 
Paper between I and M, and all the Light be- 
tween the Rays GO and HD be refraded by 
the oblique Plane of the Diamond-cut BD, 
and fall upon the Paper between K and L; 
and the Light which paffes diredly through the 
parallel Planes of the Glafs, and falls upon the 
Paper between I and M, will be border'd with 
three or more Fringes at M. 

So 



BOOK III. 297 

So by looking on the Syn through a Feather 
or black Rifcband held clofe to the Eye, feveral 
Rain-bows will appear j the Shadows which the 
Fibres or Threds caft on the T'unica Retina^ 
being border'd wi^h' the like Fringes of Co- 
lours. 

^kf'Z' When the Hair was twelve Feet diftant 
from this Hole, and its Shadow fell obliquely 
upon a flat white Scale of Inches and Parts of an 
Inch placed half a Foot beyond it, and alfo when 
the Shadow fell perpendicularly upon the fame 
Scale placed nine Feet beyond it j I meafured the 
breadth of the Shadow and Fringes as accu- 
rately as I could, and found them in Parts of an 
Inch as follows. 



The 



298 



O P T I C K S. 



At tloe I)iftance of 


hcAf a 
Foot 


Nine 
Feet 

I 
9 


The breadth of tliC Shadow 


1 


The breadth between the Middles 
of the brightefl Light of the in- 
nermofl Fringes oh either fide 
the Shadow . '^ 


h or ,\ 

I 

^3i 


1 d 

T 

I 

~l~ 

r 

?T 

I 
TT 


The breadth between the Middles 
of the brightefl Light of the 
middlemoft Fringes on either 
fide the Shadow 


The breadth between the Middles 
of the brighteft Light of the 
outmofl Fringes on either fide 
the Shadow 


I I 


The diflance between the Middles 
of the brightefl Light of the firfl: 
and fecond Fringes 




The diflance between the Middles 
of the" brightefl Light of the fe- 
cond and third Fringes 


I To 


The breadth of the luminous Part 
(green, white, yellow, and red) 
of tiie firfl Fringe 


1 70 


The bread tlx oi tne darker bpact 
between the firfl and fecond 
Fringes 


I 
140 


The breadcli of the luminous Pan 
of the fecond Fringe 


27^ 


The breadth ot the darker Space 
between the fecond and third 
Fringes 


T4~ 





Tiiefe 



BOOK III. 299 

Thefe Meafures I took by letting the Shadow 
of the Hair, at half a Foot diflance, fall fo ob- 
liquely on the Scale, as to appear twelve times 
broader than when it fell perpendicularly on it 
atthe fame diftance, and fetting down in this 
Table the twelfth part of the Meafures I then 
took. 

ObC. 4. When the Shadow and Fringes were 
caft obliquely upon a fmooth white Body, and 
that Body was removed farther and farther 
from the Hair, the firft Fringe began to appear 
and look brighter than the reft of the Light 
at the diftance of lefs than a quarter of an Inch 
from the Hair, and the dark Line or Shadow 
between that and the fecond Fringe began to 
appear at a lefs diftance from the Hair than that 
of the third part of an Inch. The fecond Fringe 
began to appear at a diftance from the Hair of 
lefs than half an Inch, oand the Shadow between 
that and the third Fringe at a diftance lefs than 
ail Inch, and the third Fringe at a diftance lefs 
than three Inches. At greater diftances they 
became much more fenlible, but kept very 
nearly the fame proportion of their breadths 
and intervals which they had at their firft ap- 
pearing. For the diftance between ♦ the middle 
of the firft, and middle of the fecond Fringe, 
was to the diftance between the middle of the 
fecond and middle of the third Fringe, as three 
to two, or ten to feven. And the laft of thefe 
two diftances was equal to the breadth of the 
bright Light or luniinous part of the firft Fringe. 
And this breadth was to the breadth of the 
bright Light of the fecond Fringe as feven to 

four, 



30O O P T I C K S. 

four, and to the dark Interval of the firft and 
fecond Fringe as three to two, and to the like 
dark Interval between the fecond and third as 
two to one. For the breadths of the Fringes 
feem'd to be in the progreffion of the Numbers 
I) v^i v^l, and their Intervals to be in the 
fame progreffion with them j that is, the Frin- 
ges and their kitervals together to be in the 
continual progreffion of the Numbers i, /?, /f, 
</!, v'i-, or thereabouts. And thefe Proportions 
held the fame very nearly at all diftances from 
the Hair ; the dark Intervals of the Fringes be- 
ing as broad in proportion to the breadth of the 
Fringes at their firil appearance as afterwards at 
great dillances from the Hair, though not fo dark 
and diftind:. • 

Obf. 5. The Sun fhining into my darken'd 
Chamber through a hole a quarter of an Inch 
broad, I placed at the diilance of two or three 
Feet from the Hole a Sheet of Pafteboard, which 
was black'd all over on both fides, and in the 
middle of it had a hole about^ three quarters 
of an Inch fquare for the Light to pafs through. 
And behind the hole I faften'd to the Palte- 
board with Pitch the blade of a ffiarp Knife, to 
intercept fome part of the Light which paffied 
through the hole. The Planes of the Pafte- 
board and blade of the Knife were parallel to 
one another, and perpendicular to the Rays. 
And when they w^re fo placed that none of 
the Sun's Light fell on the Pafteboard, but all of 
it pafied through the h.ole'to t*he Knife, and there 
part of it fell upon the blade of the Knife, and 
part of it paifed by its edge j I let this part of 

the 



BOOK III. 301 ' 

the Light which paiTed by, fall on a white Pa- 
per two or three Feet beyond the Knife, and 
there faw two ftreams of faint Light fhoot out 
both ways from the beam of Light into the flia- 
dow, like the Tails of Comets. But becaufe the 
Sun's dired: Light by its brightnefs upon the 
Paper obfcured thefe faint ftreams, fo that I 
could fcarce fee them, I made a little hole in 
the midft of the Paper for that Light to pafs 
through and fall on a black Cloth behind it ; 
and then I faw the two ftreams plainly. They 
were like one another, and pretty nearly equal 
in length, and breadth, and quantity of Light. 
Their Light at that end next the Sun's direct 
Light was pretty ftrong for the fpace of about 
a quarter of an Inch, or half an Lich, and in all 
* its progrefs from that direct Light decreafed 
gradually till it became infenfible. The whole 
length of either of thefe ftreams meafured up- 
on the Paper at the diftance of three Feet from 
the Knife was about fix or eight Inches ; fo that 
it fubtended an Angle at the edge of the Knife 
of about 10 or 12, or at moft 14 Degrees. Yet 
fometimes I thought I faw it ftioot three or four 
Degrees farther, but with a Light fo very faint 
that I could fcarce perceive it, and fufpe(5ted it 
might ( in fome meafure at leaft ) arife from 
fome other caufe than the two ftreams did. For 
placing my Eye in that Light beyond the end 
of that ftream which was behind the Knife, and 
looking towards the Knife, I could fee a line of ^ • 
Light upon its edge, and that not only when 
my Eye was in the line cf the Streams, but al- 
fo when it was without that line either towards 

the 



302 O P T I C K S. 

the point of the Knife, or towards the handle. 
This line of Light appear'd contiguous to the 
edge of the Knife, and was narrower than the 
Light of the innermofl Fringe, and narroweft 
when my Eye was fartheft from the dired: Light, 
and therefore feem'd to pafs between the Light 
of that Fringe and the edge of the Knife, and 
that which palTed nearefl the edge to be mofl . 
bent, though not all of it. 

Ohf. 6. I placed another Knife by this, fo 
that their edges might be parallel, and look to- 
wards one another, and that the beam of Light 
might fall upon both the Knives, and fome part 
of it pafs between their edges. And when the 
diflance of their edges was about the 400th 
part of an Inch, the ftream pjlrted in the mid- ^ 
die, and left a Shadow between the two parts. 
This Shadow was fo black and dark that all the 
Light which pafTed between the Knives feem'd 
to be bent, and turn'd afide to the one. hand or 
to the other. And as the Knives ftill approach'd 
one another the Shadow grew broader, and the 
ftreams ihorter at their inward ends which were 
next the Shadow, until upon the contad; of the 
Knives the whole Light vahilh'd, leaving its place 
to the Shadow. 

And hence I gather that the Light which is 
leaft bent, and goes to the inward ends of the 
ftreams, palTes by the edges of the Knives at 
the greatefh diftance, and this diflance when 
the Shadow begins to appear between the 
ftreams, is about the Sooth part of an Inch. And 
the Light which paffes by the edges of the 
Knives at diftances ftill lefs and lefs, is more and 

more 



BOOK III. 303 

more bent, and goes ta thofe parts of the 
ftreams which are farther and farther from the 
diredt Light; becaufe when the Knives approach 
one another till they touch, thofe parts of the 
ftreams vanifti laft v/hich are fartheil from the 
dired Light. 

Obf. 7. In the fifth Obfervation the Fringes 
did not appear, but by reafon of the breadth of 
the hole in the Window became fo broad as to run 
into one another, and by joining, to rriake one 
continued Light in the beginning of the ftreams. 
But in the fixth, as the Knives approached one 
another, a little before the Shadow appeared 
between- the two ftreams, the Fringes began 
to appear on the inner ends of the Streams on 
either fide of the dired: Light ; three on one 
fide made by the edge of one Knife, and three 
on the other fide made by the edge of the o- 
ther Knife. They Were diftindeft when the 
Knives were placed at the greateft diftance from 
the hole in the Window, and ftill became more 
diftind: by making the hole lefs, infomuch that 
I could fometimes fee a faint lineament of a 
fourth Fringe beyond the three above men- 
tion'd. ' And as the Knives continually ap- 
proach'd one another, the Fringes grew di- 
ftinder and larger, until they vanifh'd. The 
outmoft Fringe vanifli'd firft, and the middle- 
moft next, and the innermoft laft. And after 
they were all vanifh'd', and the line of Light 
which was in the middle between them was 
grown very broad, enlarging it felf on both fides 
into the ftreams of Light defcribed in the fifth" 
Obfervation, the above-rnention'd Shadow be- 

.1 ■ gan 



304- O P T I C K S. 

gan to appear in the middle of this line, and 
divide it along the middle into two lines of 
Li^ht, and increafed until the whole Light va- 
nilh'd. This enlargement of the Fringes was 
fo great that the Rays which go to the inner- 
moft Fringe feem'd ' to be bent above twenty • 
times more v/hen this Fringe was ready to va- 
nifh, than when one of the Knives was taken 
away. 

And from this and the former Obfervation 
compared, I gather, that the Light of the firffc 
Fringe pafTed by the edge of the Knife at a di- 
flance greater than the Sooth part of an Inch, 
and the Light of the fecond Fringe paiTed by 
the edge of the Knife at a greater diftance than 
the Light of the firft Fringe did, and that of 
the third at a greater diftance than that of the 
fecond, and that of the ftreams of Light defcri- 
bed in the fifth and fixth Obfervations pafTed by 
the edsies of the Knives at lefs diftances than that 
of any of the Fringes. 

Obf. 8. I caufed the edges of two Knives 
to be ground truly ftrait, and pricking their 
points into a Board fo that their edges might 
look towards one another, and meeting near 
their, points contain a redtilinear Angle, I faften'd 
their Handles together with Pitch to make this 
Angle invariable. The diftance of the edges of 
the Knives from one another at the diltance of 
four Inches from the angular Point, where the 
edges of the Knives met, was the eight;: part 
of an Inch j and therefore the Angle contain'd ' 
by the edges was about one Degree 54'. The 
Knives thus fix'd together I placed in a beam 

of 



BOOK III. 305 

of the Sun's Light, let into my darken'd Cham- 
ber through a Hole the 420! Part of an Inch wide, 
at the diftance of 10 or 15 Feet from the Hole, 
and let the Light which pafled between their edges 
fall very obliquely upon a fmooth white Ruler at 
the diftance of half an Inch, or an Inch from 
the Knives, and there faw the Fringes by the 
two edges of the Knives run along the edges of 
the Shadows of the Knives in Lines parallel to 
thofe edges without growing fenfibly broader, 
till they met in Angles equal to the Angle 
contained by the edges of the Knives, ai d 
where they met and joined they ended without 
croffing one another. But if the Ruler was 
held at a much greater diftance from the 
Knives, the Fringes w^here they were firther 
from the Place of their Meeting, were a little 
narrower, and became fomething broader and 
broader as they approach'd nearer and nearer to 
one another, and after they met tiiey crofs'd 
one another, and then became much broader 
than before. 

Whence I gather that the diftances at which 
the Fringes pafs by the Knives are not increafed 
nor alter'd by the approach of the Knives, but 
the Angles in whicli the Rays are there bent 
are much increafed by that approach ; and that 
the Knife which is neareli any Ray determines 
which way the Ray ftiall be bent, and the other 
Knife increafes the bent. 

Obf, 9. When the Rays fell very obliquely 
upon the Ruler at the diftance of the third Part, 
of an Inch from the Knives, the dark Line be- 
tween the firft and fecond Fringe of the Sha- 

X dow 



3o6 O P T I C K S. 

dow of one Knife, and the dark Line between 
the firft and fecond Fringe of the Shadow of 
the other Knife met with one another, at the 
diftance of the fifth Part of an Inch from th« 
end of the Light which pafTed between the 
Knives at the concourfe of their edges. And 
therefore the diftance of the edges of the Knives 
at the meeting of thefe dark Lines was the i6oth 
Part of an Inch. For as four Inches to the 
eighth Part of an Inch, fo is any Length of the 
edges of the Knives meafured from the point 
of their concourfe to the diftance of the edges 
of the Knives at the end of that Length, and fo 
is the fifth Part of an Inch to the i6oth Fart. 
So then the dark Lines above-mention'd meet 
in the middle of the Light which pafTes be- 
tween the Knives where they are diftant the 
i6oth Part of an Inch, and the one half of that 
Light pafles by the edge of one Knife at a di- 
ftance not greater than the 320th Part of an 
Inch, and falling upon the Paper makes the 
Fringes of the Shadow of that Knife, and the 
other half pafies by the edge of the other Knife, 
at a diftance not greater than the 320th Part of 
an Inch, and falling upon the Paper makes the 
Fringes of the Shadow of the other Knife. But 
if the Paper be held at a diftance from the 
Knives greater than the third Part of an Inch, 
the dark Lines above-mention'd meet at a greater 
diftance than the fifth Part of an Inch from 
the end of the Light which pafTed between the 
Knives at the concourfe of their edges ; and 
therefore the Light which falls upon the Paper 
where thofe dark Lines meet pafles between the . 

Knives 



BOOK III. 



307 



Knives where the edges are diftant above the 
160th part of an Inch. 

For at another time, when the two Knives 
were diltant eigiit Feet and five Inches from the 
little hole in the Window, made with a fmall 
Pin as above, the Light which fell upon the Pa- 
per where the aforefaid dark lines met, paffed 
between the Knives, where the dillance between 
their edges was as in the following Table, w^hen 
the diftance of the Paper from the Knives was 
alfo as follows. 



Dijiaiices of the Paper 
from the Knhes i}i 
Inches. 


Dijtances betixeen . the 
edges of the Kfiizrs in 
millefmal parts of an 
Inch. 


. 3i- 

32. 
96. 

131- 


o'oi2 

0'020 

•^ o'o34 

■ o'o^7 
o'oSi 

o'oS/ 



And hence I gather, that the Light which 
makes the Fringes upon the Paper is not the 
fame Light at all diftances of the Paper from 
the Knives, but when the Paper is held near 
the Knives, the Fringes are made by Light 
which pafTes by the edges of the Knives at a 
lefs diftance, and is more bent than when the 
Paper is held at a greater diftance from the 
Knives. 



X 2 



Obf 



3o8 OPTIC K S. 

Obf. 10. When the Fringes of the Shadows 
of the Knives fell perpendicularly upon a Paper 
at a great diftance from the Knives, they'w^ere 
in the form of Hyperbola's, and their Dimen- 
fions were as follows. Let CA, CB [in Fig. 3.] 
reprefent Lines drawn upon the Paper parallel 
to the edges of the Knives, and between which 
all the Light would fall, if it pafled between 
the edges of the Knives without inflexion ; DE 
a Right Line drawn through C making the An- 
gles A CD, BCE, equal to one another, and 
terminating all 'the Light which falls upon the 
Paper from the point where the edges of the 
Knives meet; eisy fkt^ and glv^ three hyper- 
bolical Lines reprefenting the Terminus of the 
Shadow of one of the Knives, the dark Line 
between the firft and fecond Fringes of that 
Shadow, and the dark Line between the fecond 
and third Fringes of the fame Shadow ; xip, ykq, 
and z/r, three other hyperbolical Lines repre- 
fenting the Terminus of the Shadow of the other 
Knife, the dark Line between the firfl and fecond 
Fringes of that Shadow, and the dark line be- 
tween the fecond and third Fringes of the fame 
Shadow. And conceive that thefe three Hyper- 
bola's are like and equal to the former three, and 
crofs them in the points /', i, and /, and that the 
Shadows of the Knives are terminated and diflin- 
guifh'd from the lirft luminous Fringes by the 
lines e i s and x ip, until the meeting and crof- 
fmg of the Fringes, and then thofe lines crofs 
the Fringes in the form of dark lines, termina- 
ting the firft luminous Fringes within fide, and 
diftinguifhing them from another Light which 

begins 



BOOK III. 309 

begins to appear at /, and illuminates all the 
triangular fpace /j^DEj. comprehended by thefe 
dark lines, and the right line DE. Of thefe 
Hyperbola's one Afymptote is the line DE, and 
their other Afymptotes are parallel to the lines 
C A and C B. Let r 'v reprefent a line drawn 
any where upon the Paper parallel to the Afym- 
ptote DE, and let this line crofs the right lines 
AC in w, and B C in «, and the fix dark hy- 
perbolical lines in />, ^, ^ 3 J, ^, i' ; and by mea- 
suring the diftances /) J, gt, r'-j, and thence 
collecting the lengths of the Ordinates n p, n q^ 
nr or m s^ m /, m v^ and doing this at feveral 
diftances of the line r v from the Afymptote DD, 
you may find as many points of thefe Hyperbo- 
la's as you pleafe, and thereby know that thefe 
curve lines are Hyperbola's differing little from 
the conical Hyperbola. And by meafuring the 
lines C /, C k, C /, you may find other points of 
thefe Curves. 

For inftance; when the Knives were diftant 
from the hole in the Window ten Feet, and the 
Paper from the Knives nine Feet, and the An- 
gle contained by the edges of the Knives to 
which the Angle ACBis equal, was fubtend- 
ed by a Chord which was to the Radius as i 
to 32, and the diftance of the line rv from the 
Afymptote DE was half an Inch: I meafured 
the lines pSy qt, rv, and found them 0*35, 
o'65, o'98 Inches refped;ively ; and by adding 
to their halfs the line r m n^ ( w^hich here was 
the 128th part of an Inch, or 0*0078 Inches,) the 
Sums «^, nq^nVy were o' 1828, ©'3328, 0*4978 
Inches. I meafured alfo the diftances of the 

X 3 brighteft 



3IO O P T I C K S. 

brightefl parts of the Fringes which run between 
fq and st, qr and t 'U, and next beyond r and 'u> 
and found them o'5, o'B, and iij Inches. 

Obf. II. The Sun fhining into my darkened 
Room through a fmall round hole made in a 
Plate of Lead with a flender Pin, as above ; I 
placed at the hole a Prifm to refrad the Light, 
and form on the oppofite Wall the Spedtrum 
of Colours, defcribed in the third Experiment 
of the firft Book. And then I found that the 
Shadows of all Bodies held in the colour'd 
Light between the Prifm and the Wall, were 
border'd with Fringes of the Colour of that 
Light in which they were held. In the full red 
Light they were totally red without any fenfi- 
ble blue or violet, and in tiie deep blue Light 
they were totally blue without any fenfible red 
or yellow ; and fo in the green Light they were 
totally green, excepting a little yellow and blue, 
which were mixed .in the green Light of the 
Prifm. And comparing the Fringes made in 
the feveral colour'd Lights, I found that thofe 
made in the red Light were largeft, thofe 
made in the violet were leail, and thofe made 
-in the green Vv^ere of a middle bignefs. For 
the Fringes with which the Siradow of a Man's 
Hair were bordered, being meafured crofs the 
Shadow at the diftance of fix Liches from the 
Hair, the diflance between the middle and moil; 
luminous part of the iirfl or innermoft Fringe 
on one. fide of the Shadow, and that of the like 
Fringe on the other iide of the Shadow, was in 

the full red Lieht -~ of an Inch, and in the full 

violet 



BOOK III. 311 

violet ?V. And the like diftance between the 
middle and mofl luminous parts of the fecond 
Fringes on either iide the Shadow was in the full 
red Light »'=-, and in the violet tV of an Inch. 
And thefe diftances of the Fringes held the fame 
proportion at all diftances from the Hair without 
any fenfible 'variation. 

So then the Rays which made thefe Fringes 
in the red Light paffed by the Hair at a greater 
diftance than thofe did which made the like 
Fringes in the violet j and therefore the Hair 
in caufing thefe Fringes adied alike upon the 
red Light or leaft refrangible Rays at a greater 
diftance, and upon the violet or moft refrangi- 
ble Rays at a lefs diftance, and by thofe adions 
difpofed the red Li^ht into larger Fringes, and 
the violet into fmaller, and the Lights of inter- 
mediate Colours into Fringes of intermediate big- 
neftes without changing the Colour of any fort 
of Light. 

When therefore the Hair in the firft and fe- 
cond of thefe Obfervations was held in the 
white beam of the Sun's Light, and caft a Sha- 
dow which was border'd with three Fringes of 
coloured Light, thofe Colours arofe not from 
any new modifications imprefs'd upon the Rays 
of Light by the Hair, but only from the vari- 
ous inflexions whereby the feveral Sorts of Rays 
were feparated from one another, which before 
feparation, by the mixture of all their Colours, 
compofed the white beam of the Sun's Light, 
but whenever feparated compofe Lights of the 
feveral Colours which they are originally difpo- 
fed to exhibit. In this i ithObfervation, where 

X 4 the 



312 O P T I C K S. 

!Dhe Colours are feparated before the Light paf- 
fes by the Hair, the leaft refrangible Rays, which 
when feparated from the reft make red, were 
infleded at a greater diftance from the Hair, fo 
as to make three red Fringes at a greater di- 
ftance from the middle of the Shadow of the 
Hair j and the moft refrangible Rays which 
when feparated make violet, were inflected at 
a lefs diftance from the Hair, fo as to make 
three violet Fringes at a lefs diftance from the 
middle of the Shadow of the Hair. And other 
Rays of intermediate degrees of Refrangibility 
were inflefted at intermediate diftances from 
the Hair, fo as to make Fringes of intermediate 
Colours at intermediate diftances from the mid- 
dle of the Shadow of the Hair. And in the 
fecond Obfervation, where all the Colours are 
mix'd in the white Light which pafles by the 
Hair, thefe Colours are feparated by the vari- 
ous inflexions of the Rays, and the Fringes 
which they make appear all together, and the 
innermoft Fringes being contiguous make on^^ 
broad Fringe compofed of all the Colours in . 
due order, the violet lying on the infide of the 
Frmge next the Shadow, the red on the out- 
fide fartheft from the Shadow, and the blue, 
green, and yellow, in the middle. And, in like 
manner, the middlemoft Fringes of all the Co- 
lours lying in order, and being contiguous, 
make another broad Fringe compofed of all the 
Colours -J and the outm.oft Fringes of all the 
Colours lying in order, and being contiguous, 
make a third broad Fringe compofed of all the 
Colours. Thefe are the three Fringes of co- 

lour'd 



BOOK III. 313 

lour'd Light with which the Shadows of all Bo- 
dies are border'd in the fecond Cbfervation. 

When I made the foregoing Obfervations, I 
defign'd to repeat moft of thcm.with more care 
and exadnefs, and to mJike fome new ones for 
determining the manner how the Rays of Light 
are bent in their palTage by Bodies, for making 
the Fringes of Colours with the dark lines be- 
tween them. But I was then interrupted, and 
cannot now think of taking thefe things into far- 
ther Confideration. And fince 1 have not finifh'd 
this part of my Defign, I fhall conclude with 
propofing only fome Queries, in order to a far- 
ther fearch to be made by odiers. 

^ery i. Do not Bodies a<5t upon Light at 
a diltance, and by their action bend irs Raysj and 
is not this action ( cceteris paribus ) flrongeft at 
the leaft diftance ? 

^. 2. Do not the Rays which differ in Re- 
frangibility differ alfo in Flexibity j and are they 
not by their different Inflexions feparatcd from 
one another, fo as after feparation to niake the 
Colours in the three Fringes above defer ibed ? 
And after what manner are they infle(5ted to make 
thofe Fringes ? 

^. 3 Are not the Rays of Light in pafling 
by the edges and fides of Bodies, bent feveral 
times backwards and forwards, with a motion 
like that of an Eel ? And do not the three Frin- 
ges of colour'd Light above-mention'd arife from 
three fuch bendings ? 

^. 4. Do not the Rays of Light which fall 
upon Bodies, and are refleded or refraded, be- 
gin 



314 O P T I C K S. 

gin to bend before they arrive at the Bodies ; and 
are they not reflecfled, refrafted, and infledied, 
by one and the fame Principle, ading varioufly 
in various Circumftances ? 

^. 5. Do not Bodies and Light ad mutually 
upon one another ; that is to fay. Bodies upon 
Light in emitting, receding, refrading and in- 
fleding it, and Light upon Bodies for heating 
them, and putting their parts into a vibrating 
motion vs^herein heat confifts ? 

^. 6. Do not black Bodies conceive heat 
more eafily from Light than thofe of other Co- 
lours do, by reafon that the Light falling on them 
is not refleded outw^ards, but enters the Bodies, 
and is often refleded and refraded within them, 
until it be ftifled and loft ? 

^. 7. Is not the ftrength and vigor of the 
a^ion between Light and fulphureous Bodies ob- 
ferved above, one reafon why fulphureous Bodies 
take fire more,readily, and burn more vehement- 
ly than other Bodies do ? 

^. 8. Do not all fix'd Bodies, when heated 
beyoiifl a certain degree, emit Light and fhine ; 
and is not this Emiffion perform'd by the vi- 
brating motions of their parts ? And do not all 
Bodies which abound with terreflrial parts, and 
efpecially with fulphureous ones, emit Light 
as often as thofe parts are fufficiently agitated j 
whether that agitation be made by Heat, or by 
Fridicn, or Percuffion, or Putrefadion, or by 
any vital Motion, or any other Caufe? As for 
infliance ; Sea- Water in a raging Storm ; Quick- 
filver agitated in ^jacuo ; the Back of a Cat, or 
Neck of a Horfe, obliquely ftruck or rubbed in 

a dark 



BOOK III. 315 

a dark place ; Wood, Flefh and Fifli while they 
putrefy ; Vapours ariling from putrefy 'd Wa- 
ters, ufually call'd Ignes Fatui ; Stacks of moifl 
Hay or Corn growing hot by fermentation ; 
Glcfw-worms and the Eyes of fome Animals by 
vital Motions J the vulgar Phofphoriis agitated 
by the attrition of any Body, or by the acid 
Particles of the Air; Amber and fome Dia- 
monds by ftriking, preffing or rubbing them; 
Scrapings of Steel ftruck off with a Flint ; Iron 
hammer'd very nimbly till it become fo hot as 
to kindle Sulphur thrown upon it ; the Axle- 
trees of Chariots taking fire by the rapid rota- 
tion of the Wheels ; and fome Liquors mix'd 
with one another whofe Particles come toge- 
ther with an Impetus, as Oil of Vitriol diftilled 
from its weight of Nitre, and then mix'd with 
twice its weight of Oil of Annifeeds. So alfo a 
Globe of Glafs about 8 or 10 Inches in diameter, 
being put into a Frame where it may be fwiftly 
turn'd round its Axis , will in turning fhine 
where it rubs againft the palm of ones Hand 
apply 'd to it: And if at the fame time a <^iece 
of white Paper or white Cloth, or the end of 
ones Finger be held at the diftance of about a 
quarter of an Inch or half an Inch from that 
part of the Glafs where it is mojft in motion, 
the eled:rick Vapour which is excited by the 
fri6lion of the Glafs againft the Hand, will by 
dafhing againft the white Paper, .Cloth or Fin- 
ger, be put into fuch an agitation as to emit 
Light, and make the white Paper, Cloth or Fin- 
ger, appear lucid like a Glow-worm ; and in 
rufhing out of the Glafs will fometimes pufti 

againft 



3i6 * O P T I C K S. 

againft the Finger fo as to be felt. And the fame 
things have been found by rubbing a long and 
large Cylinder of Glafs or Amber with a Paper 
held in ones hand, and continuing the fridiion till 
the Glafs grew warm. 

^. 9. Is not Fire a Body heated fo hot as to 
emit Light copioufly? For what elfe is a red hot 
Iron than Fire? And what elfe is a burning Coal 
than red hot Wood ? 

§u. 10. Is not Flame a Vapour, Fume or Ex- 
halation heated red hot, that is, fo hot as to 
fhine ? For Bodies do not flame without emit- 
ting a copious Fume, and this Fume burns in 
the Flame. The Igms Fatuus is a Vapour fhi- 
ning without heat, and is there not the fame 
difference between this Vapour and Flame, as 
between rotten Wood fhining without heat and. 
burning Coals of Fire ? In diftilling hot Spirits, 
if the Head of the Still be taken off, the Va- 
pour which afcends out of the Still will take fire 
at the Flame of a Candle, and turn into Flame, 
and the Flame will run along the Vapour from 
the Candle to the Still. Some Bodies heated by 
Motion or Fermentation, if the heat grow in- 
renfe, fume copioufly, and if the heat be great 
enough the Fumes will (liine and become Flame. 
Metals in fuflon do not flame for want of a co- 
pious Fume, except Spelter, which fumes co- 
pioufly, and thereby flames. All flaming Bo- 
dies, as Oil, Tallow, Wa"^, Wood, foffil Coals, 
Pitch, Sulphur, by flaming waflie and vanifli in- 
to burning Smoke, which Smoke, if the Flame 
be pur out, is very thick and vifible, and fome- 
times fmells ftrongly, but in the Flame lofes its 

fmell 



BOOK III. 317 

fmell by burning, and according to the nature 
of the Smoke the Flame is of feveral Colours, 
as that of Sulphur blue, that of Copper open'd 
with fublimate green, that of Tallow yellow, 
that of Camphire white. Smoke paffing through 
Flame cannot but grow red hot , and red hot 
Smoke can have no other appearance than that 
of Flame. When Gun-powder takes fire, it 
goes away into flaming Smoke. For the Char- 
coal and Sulphur eafily take fire, and fet fire to 
the Nitre, and the Spirit of the Nitre being 
thereby rarified into Vapour , ruflies out with 
Explofion much after the manner that the Va- 
pour of Water rufhes out of an ^olipile^ the 
Sulphur alfo being volatile is converted into 
Vapour, and augments the Explofion. And 
the acid Vapour of the Sulphur (namely that 
which diftils under a Bell into Oil of Sulphur,) 
entring violently into the fix'd Body of the Ni- 
tre, fets loofe the Spirit of the Nitre, and ex- 
cites a great Fermentation, whereby the Heat 
is farther augmented, and the fix'd Body of the 
Nitre is alfo rarified into Fume, and the Explo- 
fion is thereby made more vehement and quick. 
For if Salt of Tartar be mix'd with Gun-pow- 
der, and that Mixture be warm'd till it takes 
fire, the Explofion will be more violent and 
quick than that of Gun-powder alone; which^ 
cannot proceed from any other caufe than the 
action of the Vapour of the Gun-powder upon 
the Salt of Tartar, whereby that Salt is rarified. 
The Explofion of Gun-powder arifes therefore 
from the violent aftion whereby all the Mixture 
being quickly and vehemently heated, is rarified 

r and 



3i8 O P T I C K S. 

and converted into Fume and Vapour: which 
Vapour, by the violence of that adiion , be- 
coming fo hot as to fhine, appears in the form of 
Flame. 

^. 1 1. Do not great Bodies conferve their 
heat the longeft, their parts heating one ano- 
ther, and may not great denfe and fix'd Bo- 
dies, when heated beyond a certain degree, e- 
mit Light fo copioufly, as by the Emilfion and 
Re-a6tion of its Light, and the Reflexions and 
Refradions of its Rays within its Pores to grow 
ilill hotter, till it comes to a certain period of 
heat, fuch as is that of the Sun ? And are not 
the Sun and fix'd Stars great Earths vehemently 
hot, whofe heat is conferved by the greatnef^ 
of the Bodies, and the mutual Adiion and Re- 
action between them, and the Light which they 
emit, and whofe parts are kept from fuming a- 
way, not only by their fixity, but alfo by the 
vaft weight and denfity of the Atmofpheres in- 
cumbent upon them ; and very ftrongly com- 
preffing them, and condenfing the Vapours and 
Exhalations which arife from them? For if 
Water be made warm in any pellucid Veflel 
emptied of Air, that Water in the Vacuum will 
bubble and boil as vehemently as it would in 
the open xAir in a Veffel fet upon the Fire till 
it conceives a much greater heat. For the 
weight of the incumbent Atmofphere keeps 
down the Vapours, and hinders the Water from 
boiling, until it grow much hotter than is re- 
quifite to make it boil in vacuo. Alfo a mix- 
ture of Tin and Lead being put upon a red hot 
Iron in vacuo emits a Fume and Flame^ but the 
3 fame 



BOOK III. 319 

fame Mixture in the open Air, by reafon of the 
incumbent Atmofphere, does not fo much as e- 
mit any Fume which can be perceived by Sight. 
In like manner the great weight of the Atmo- 
fphere which lies upon the Globe of the Sun 
may hinder Bqdies there from riling up and 
going away from the Sun in the form of Va- 
pours and Fumes, unlefs by means of a far 
greater heat than that which on the Surface of 
our Earth would very eafily turn them into Va- 
pours and Fumes. And the fime great weight 
may condenfe thofe Vapours and Exhalations as 
foon as they fliall at any time begin to afcend 
from the Sun, and make them prefently fall 
back again into him, and by that adion increafe 
his Pleat much after the manner that in our 
Earth the Air increafes the Heat of a culinary 
Fire. And the fame weight may hinder the 
Globe of the Sun from being diminifh'd, unlefs 
by the Emiflion of Light, and a very fmall quan- 
tity of Vapours and Exhalations. 

%/. 12. Do not the Rays of Light in falling 
upon the bottom of the Eye excite Vibrations 
in the Tunica Retina? Which Vibrations, be- 
ing propagated along the folid Fibres of the op- 
tick Nerves into the Brain, caufe the Senfe of 
feeing. For becaufe denfe Bodies conferve their 
Heat a long time, and the denfeft Bodies con- 
ferve their Heat the longeft, the Vibrations of 
their parts are of a lalling nature, and there- 
fore may be propagated along folid Fibres of 
uniform denfe Matter to a great diftance, for 
conveying into the Brain the impreffions made 
upon all the Organs of Senfe. For that Motion 

which 



320 O P T I C K S. 

which can continue long in one and the fame part 
of a Body, can be propagated a long way from 
one part to another, fuppofing the Body homo- 
geneal, fo that the Motion may not be refleded, 
reffaded, interrupted or diforder'd by any un- 
evennefs of the Body. 

^. 13. Do not feveral forts of Rays make 
Vibrations of feveral |)ignefres, which according 
to their bignelfes excite Senfations of feveral Co- 
lours, much after the manner that the Vibrations 
of the Air, according to their feveral bignelfes 
excite Senfations of feveral Sounds ? And parti- 
cularly do not the moft refrangible Rays excite 
the fhorteft Vibrations for making a Senfation of 
deep violet, the leafl refrangible the largeft for 
making a Senfation of deep red, and the feveral 
intermediate forts of Rays, Vibrations of feveral 
intermediate bigneffes to make Senfations of the 
feveral intermediate Colours ? 

^. 14. May not the harmony and difcord of 
Colours arife from the proportions of the Vibra- 
tions propagated through the Fibres of the op- 
tick Nerves into the Brain, as the harmony and 
difcord of Sounds arife from the proportions of 
the Vibrations of the Air? For fome Colours, if 
they be view'd together, are agreeable to one 
another, as thofe of Gold and Indigo, and others 
difagree. 

^i. 15. Are not the Species of Objedls feen 
with both Eyes united where the optick Nerves 
meet before they come into the Brain, the Fi- 
bres on the right fide of both Nerves uniting 
there, and after union going thence into the 
Brain in the Nerve whicji is on the right fide of 

thq 



BOOK III. .21 

the Head, and the Fibres on the left fide of 
both Nerves uniting in the fame place, and af- 
ter union going into the Brain in the Nerve 
which is on the left fide of the Head, and thefe 
tw^o Nerves meeting in the Brain in fuch a man- 
ner that their Fibres make but one entire Spe- 
cies or Pidure, half of which on the right fide 
of the Senforium comes from the right fide of 
both Eyes through the right fide of both op- 
tick Nerves to the place where the Nerves meet, 
end from thence on the right fide of the Head 
into the Brain, and the other half on the left 
fide of the Senforium comes in like manner from 
the left fide of both Eyes. For the op tick 
Nerves of fuch Animals as look the fame way 
with both Eyes (as of Men, Dogs, Sheep, Oxen, 
&c\) meet before they come into the Brain, but 
the optick Nerves of fuch Animals as do not 
look the fame way with both Eyes (as of Fifiics, 
and of the Chameleon,) do not meet, if I am 
rightly inform'd. 

^. 1 6. When a Man in the dark prefTes either 
corner of his Eye with his Finger, and turns his 
Eye away from his Finger, he will fee a Circle 
of Colours like thofe in the Feather of a Pea- 
cock's Tail. If the Eye and the Finger remain 
quiet thefe Colours vanifh in a fecond Minute of 
Time, but if the Finger be moved with a qua- 
vering Motion they appear again. Do not thefe 
Colours arife from fuch Motions excited in the 
bottom of the Eye by the PrelTure and Motion 
of the Finger, as at other times are excited 
there by Light for caufing Vifion ? And do not 
the Motions once excited continue about a Se- 

,y cond 



322 O P T I C K S. 

cond of Time before they ceafe ? And when a 
Man by a ftroke upon his Eye fees a flafh of 
Light, are not the Hke Motions excited in the 
Retina by the ftroke ? And when a Coal of Fire 
moved nimbly in the circumference of a Cir- 
cle, makes the whole circumference appear like 
a Circle of Fire ; is it not becaufe the Motions 
excited in the bottom of the Eye by the Rays 
of Light are of a lafting nature, and continue 
till the Coal of Fire in going round returns to 
its former place ? And confidering the lafting- 
nefs of the Motions excited in the bottom of 
the Eye by Light, are they not of a vibrating 
nature ? 

%/. 17. If a Stone be thrown into ftagnating 
Water, the Waves excited thereby continue- 
fome time to arife in the place where the Stone 
fell into the Water, and are propagated from 
thence in concentrick Circles upon the Surface 
of the Water to great diftances. And the Vi- 
brations or Tremors excited in the Air by per- 
cuffion, continue a little time to move from the 
place of percufTion in concentrick Spheres to 
great diftances. And in like manner, when a Ray 
of Light falls upon the Surface of any pellucid 
Body, and is there refra(fted or reflected, may not 
Waves of Vibrations, or Tremors, be thereby 
excited in the refracting or reflecfling Medium at 
the point of Incidence, and continue to arife 
there, and to be propagated from thence as long 
as they continue to arife and be propagated, when 
they are excited in the bottom of the Eye by the 
Prellure or Motion of the Finger, or by the Light 
which comes from the Coal of Fire in the Ex- 
periments. 



B o o ic in. 323 

perimetits abovemention'd ? and are not thefa 
Vibrations propagated from the point of Inci- 
dence to great diltances ? And do they not over- 
take the Rays of Light, and by overtaking them 
fucceffively, do they not put them into the Fits 
of eafy Reflex io.^. and eafy Tranfmiinon defcribed 
above? For if the Rays endeavour to recede from 
the denfeft part of the Vibration, they may be 
ahernately accelerated and retarded by the Vi- 
brations overtaking them. 

%. 18. If in two large tall cylindrical Vef-* 
fels of Glafs inverted, two little Thermometers 
be fufpended fo as not to touch the Veffels, and 
the Air be drawn out of one of thefe Veffels, 
and thefe Veffels thus prepared be carried out 
of a cold place into a warm one; the Thermo- 
meter ift 'Vacuo will grov/ warm as much, and 
almoft as foon as the Thermometer which is 
not in vacuo. And when the Veffels are carri- 
ed back into the cold place, the Thermometer 
in vacuo will grow cold almofi: as foon as the 
other Thermometer. Is not th^e Heat of the 
warm Room convey'd through the Vacuum by 
the Vibrations of a much fubriler Medium than 
Air, which after the Air was drawn out remain- 
ed in the Vacuum f And is not this Medium the 
fame with that Medium by which Light is re- 
fracted and refleded, and bv whofe Vibrations 
Light communicates Heat to Bodies, and is 
put into Fits of eafy Reflexion and eafy Tranf- 
miffion ? And do not the Vibrations of this Me-* 
dium in hot Bodies contribute to the intenfenefs 
and duration of their Heat ? And do not hot 
Bodies communicate their Heat to contiguous 

y 3 cdld 



324 O P T I C K S. 

cold ones, by the Vibrations of this Medium 
propagated from them into the cold ones ? And 
is not this Medium exceedingly more rare and 
fubtile than the Air, and exceedingly more ela- 
ftick and adlive? And doth it not readily per- 
vade all Bodies? And is it not ( by its elaftick 
force) expanded through all the Heavens ? . 

^. 19. Doth not the Refradtion of Light 
proceed from the different denfity of this JEzhe- 
real Medium in different places, the Light re- 
ceding always from the denfer parts of the Me- 
dium? And is not the denfity thereof greater 
in free and open Spaces void of Air and other 
groffer Bodies, than vi^ithin tjie Pores of Wa- 
ter,' Glafs, Cryflal, Gems, and other compacfl 
Bodies? For w^hen Light paffes through Glafs 
or Cryflal, and falling very obliquely upon the 
farther Surface thereof is totally refleded, the 
total Reflexion ought to proceed rather from the 
denfity and vigour of the Medium w^ithout and 
beyond the Glafs, than from the rarity and w^eak- 
nefs thereof 

^. 20. Doth not this Ethereal Medium in 
paffing out of Water, Glafs, Cryflal, and other 
compad: and denfe Bodies into empty Spaces, 
grov^ denfer and denfer by degrees, and by that 
means refraft the Rays of Light nor in a point, 
but by bending them gradually in curve Lines ? 
And doth not the gradual condcnfation of this 
Medium extend to fome diflance from the Bo- 
dies, and thereby caufe the Inflexions of the 
Rays of Light, which pafs by the edges of denfe 
Bodies, at fome diflance from the Bodies ? 



^. 



BOOK III. 325 

^. 21. Is not this Medium much rarer with- 
in the denfe Bodies of the Sun, Stars, Planets 
and Comets, than in the empty celeftial Spaces 
between them ? And in pafling from them to 
great diftances , doth it not grow denfer and 
denfer perpetually, and thereby caufe the gra- 
vity of thofe great Bodies towards one another, 
and of their parts towards the Bodies; every 
Body endeavouring to go from the denfer parts 
of the Medium towards the rarer ? For if this 
Medium be rarer within the Sun's Body than at 
its Surface, and rarer there than at the hun- 
dredth part of an Inch from Its Body, and ra- 
rer there than at the fiftieth part of an Inch ftom 
its Body, and rarer there than at the Orb of 
Saturn, I fee no reafon why the Increafe of 
denfity fhould flop any where, and not rather 
be continued through all diftances from the Sun 
to Saturn^ and beyond. And though this In- 
creafe of denfity may at great diftances be ex- 
ceeding flow, yet if the elaftick force of this 
Medium be exceeding great, it may fufhce to 
impel Bodies from the denfer parts of the Me- 
dium towards the rarer , with all that power 
which we call Gravity. And that the elaflick 
force of this Medium is exceeding great, may 
be gather'd from the fwiftnefs of its Vibrations. 
Sounds move about 1 140 EnMh Feet in a fe- 
cond Minute of Time, and in feven or eight 
Minutes of Time they move about one hundred 
Englijlo Miles. Light moves from t':e Sun to 
us in about feven or eight Minutes f Time, 
which diflance is about 70000000 Eng jh Miles, 
fuppofing the horizontal Parallax of tiic Sun to 

Y 3 be 



3^6 O P T I C K S, 

be about 12". And the Vibrations or Pulfes of 
this Medium, that they may caufe the akernatc 
Fits of eafy TraDfiriillion and eafy Reflexion, . 
muft be fwlJtcr th; n Light, and by confequencc 
above 700000 amL?. fwiirer.than Sounds. And 
therefore the eUitick force of this Medium, in 
proportion to its denfiiy, muft be above 70000Q 
X 700000 (that is, above 490000000000) times 
greater than the elaftick force of the Air is in 
proportion to its deufity. For the Velocities of 
the Puh'es of ehifticiv Mediums are in a fubdupU^ 
cate Ratio of the Hlailiciries and the Rarities of 
the Mediums taken together. 

As Attraction is ilronger in fmall Magnets 
than in great ones in proportion to their Bulk, 
and Gravity is greater in the Surfaces of fmall 
Planets than in thofe of great ones in propor- 
tion to their bulk, and fmall Bodies are agita- 
ted much more by eledric attradion than great 
ones J fo the fmallnefs of the Rays of Light 
may contribute very much to the power of 
the Agent by which they are refraded. And 
fo if any one fhould fuppofe that Mther ( like 
our Air) may contain Particles which endeavour 
to recede from one another ( for J do not know 
what this Mther is) and that its Particles are 
exceedingly fmaller than thofe of Air, or even 
than thofe of Light: The exceeding fmallnefs 
of its Particles may contribute to the greatnefs 
of the force by which thofe Particles may re-, 
cede from one anqther, and thereby make that 
Medium exceedingly more rare and elaftick 
than Air, and by confequence exceedingly lefs 
able to refift the motions of Projediles, and 

exceed- 



BOOK III. 327 

exceedingly more able to prefs upon grofs Bodies, 
by endeavouring to expand it lelf. 

^/. 22. May not Planets and Comets, and all 
grofs Bodies, perform their Motions more freely, 
and with lefs refiftance in this ^Ethereal Medium 
than in any Fluid, which fills all Space ade- 
quately without leaving any Pores, and by confe- 
quence is much denfer than Quick'-lilver or Gold? 
And may not its refiftance be fo fmall, as to be 
inconfiderable ? Forinftance; 1£ this Mther (for 
fo I will call it ) fhould be - fuppofed 700000 
times more elaftick than our Air, and above 
700000 times more rare j its refiftance would 
be above 600000000 times lefs than that of Wa- 
ter. And fo fmall a refiftance would fcarce 
make any fenfible alteration in the Motions of 
the Planets in ten thoufand Years. If any one 
would ask how a Medium can be fo rare, let 
him tell me how the Air, in the upper parts of 
the Atmofphere, Qin be above an hundred thou- 
fand thoufand times rarer than Gold. Let him 
alfo tell me, how an eledtrick Body can by Fri- 
ction emit an Exhalation fo rare and fubtile, and 
yet fo potent, as by its Emiflion to caufe no 
fenftble Diminution of the weight of the de- 
rrick Body, and to be expanded through a 
Sphere, whofe Diameter is above two Feet, and 
yet to be able to agitate and carry up Leaf Cop- 
per, or Leaf Gold, at the diftance of above a 
Foot from the eledrick Body? And how the 
Effluvia of a Magnet can be fo rare and fubtile, as 
to pafs through a Plate of Glafs without any Reii- 
ftance or Diminution of their Force, and vet fo 
potent as to turn a magnetick Needle beyond the 
Glafs? y 4 ^, 



328 P T I C K S. 

^/. 23. Is not Vifion perform'd chiefly by the 
Vibrations of this Medium, excited in, the bot- 
tom of the Eye by the Rays of Light, and pro- 
pagated through the folid, pellucid and uniform 
Capillamenta of the optick Nerves into the place 
of Senfaticn ? And is not Hearing perform'd by 
the Vibrations either of this or fome other Medi- 
um, excited in the auditory Nerves by the Tre- 
mors of the Air, and propagated through the fo- 
lid, pellucid and uniform Capillamenta of thofe 
Nerves into the place of Senfatiofi ? And fo of 
the other Senfes. 

^. 24. Is not Animal Motion perform'd by 
the Vibrations of this Medium, excited in the 
Brain by the power of the Will, and propaga- 
ted from thence through the folid, pellucid and 
uniform Capillamenta of the Nerves into the 
Mufcles, for contrad:ing and dilating them ? I 
fuppofe that the Capillamenta of the Nerves are 
each of them folid and uniform, that the vibra- 
ting Motion of the iEthereal Medium may be 
propagated along them from one e;id to the other 
uniformly, and w^ithout interruption: For Ob- 
ftrudions in the Nerves create Palfies. And that 
they may be Sufficiently uniform , I fuppofe 
them to be pellucid when view'd fmgly, tho' the 
Reflexions in their cylindrical Surfaces may make 
the whole Nerve ( compofed of many Capilla- 
menta) appear opake and white. For opacity 
.arifes from reflecting Surfaces, fuch as may di- 
fturb and interrupt the Motions of this Medium. 

^/. 25. Are there not other original Proper- 
ties of the Rays of Light, befides thofe alrea- 
dy defcribed ? An inftance of another original 

Fro- 



BOOK III. 329 

Property we have in the Refradion of Illand 
Cryftal , defcribed firft by Erajmm Bartholine^ 
and afterwards more exadly by Hugeniin^ in his 
Book De la Lumiere, This Gryftal is a pel- 
kicid fiffile Stone, clear as Water or Cryftal of 
the Rock, and without Colour j enduring a red 
Heat without lofing its tranfparency, and in a 
very ftrong Heat calcining without Fufion. 
Steep'd a Day or two in Water, it lofes its na- 
tural Polifh. Being rubb'd on Cloth, it attracfls 
pieces of Straws and other light things, like Am- 
bar or Glafs; and with Aqua Jortis it makes an 
Ebullition. It feems to be a fort of Talk, and 
is found in form of an oblique Parallelopiped, 
with lix parallelogram Sides and eight folid An- 
gles. The obtule Angles of the Parallelograms 
are each of them 10 1 Degrees, and 52 Minutes; 
the acute ones 78 Degrees and 8 Minutes. Two 
of the folid Angles oppofite to one another, as 
C and E, are compalTed each of 
them with three of thefe obtufe ^'* '/£""" 
Angles, and each of the other 
fix with one obtufe and two acute ones. It 
cleaves eaiily in planes parallel to any of its 
Sides, and not in any other Planes. It cleaves 
with a glofly polite Surface not perfectly plane, 
but with fome little unevennefs. It is eafily 
fcratch'd, and by reafon of its foftnefs it takes a 
Polifh very difficultly. It polifhes better upon 
polifh'd Looking-glafs than upon Metal, and 
perhaps better upon Pitch, Leather or Parch- 
ment. Afterwards it muft be rubb'd with a lit- 
tle Oil or white of an Egg, to fill up its Scratches; 
whereby it will become very tranfparent and po- 
lite. 



330 



O P T I C K S. 



lite. But for feveral Experiments, it is not necef- 
fary to polifh it. If a piece of this cryflalline 
Stone be laid upon a Book, every Letter of the 
Book feen through it will appear double, by 
means of a double Refracflion. And if any beam 
of Light falls either perpendicularly, or in any 
oblique Angle upon any Surface of this Cryftal, 
it becomes divided into two beams by means of, 
the fame double Refraction. Which beams are of 
the fame Colour with the incident beam of Light, 
and feem equal to one another in the quantity of 
their Light, or very nearly equal. One of thefe 
Refra<flions is perform'd by the ufual Rule of Op- 
ticks, the Sine of Incidence out of Air into this 
Cryftal being to the Sine of Refradion, as five to 
three. The other Refra(5tion, which may be cal- 
led the unufual Refraction, is perform'd by the 
following Rule. 

5\ 




H ^ 

Let ADBC reprefent the refrading Surface 

of 
\ 



BOOK III. 331 

of the Cryftal, C the biggeft folid Angle at that 
Surface, GEHF the oppofite Surface, and CK 
a perpendicular on that Surface. This perpen- 
dicular makes with the edge of the Cryftal C F, 
an Angle of 19 Degr. 3'. Join KF, and in it 
take KL, fo that the Angle KCL be 6 Degr. 
40'. and the Angle LCF 12 Degr. 23'. And if 
ST reprefent any beam of Light incident at T 
in any Angle upon the refracfting Surface AD B C, 
let TV be the refradted beam determin'd by the 
given Portion of the Sines 5 to 3, according to 
the ufual Rule of Opticks. Draw V X parallel 
and equal to KL. Draw it the fame way from 
V in which L liethfromK; and joining TX, 
this line T X fhall be the other refracted beam 
carried from T to X, by the unufual Refra- 
d;ion, 

If therefore the incident beam S T be perpen- 
dicular to the refra(5ling Surface, the two beams 
TV and TX, into which it fhall become di- 
vided, fliall be parallel to the lines CK and CL ; 
one of thofe beams going through the Cryftal 
perpendicularly, as it ought to do by the ufual 
Laws of Opticks, and the other T X by an unu- 
fual Refradion diverging from the perpendicular, 
and making with it an Angle V T X of about 6 1 
Degrees, as is found by Experience. And 
hence, the Plane VTX, and fuch like Planes 
which are parallel to the Plane C F K, may be 
called the Planes of perpendicular Refradion. 
And the Coaft towards which the lines KL and 
VX are drawn, may be call'd the Coaft of unu- 
fual Refraction. 

In like manner Cryftal of the Hock has a 
5 double 



332 O P T I C K S. 

double Refra(5tion : But the difference of tl^ two 
Refradions is not fo great and manifefl as in 
Ifland Cryftal. 

When the beam S T incident on Ifland Cry- 
ftal is divided into two beams T V and T X, 
and thefe two beams arrive at the farther Surface 
of the Giafs ; the beam T V, which was refra- 
cted at the firfl Surface after the ufual manner, 
Ihall be again refracted entirely after the ufual 
manner at the fecond Surface ; and the beam T X, 
which was refracted after the unufual manner in 
the firft Surface, lliall be again refradlied entirely 
after the unufual manner in the fecond Surface ; 
fo that both thefe beams fliall emerge out of the 
lecond Surface in lines parallel to the firft incident 
beam S T. 

And if two pieces of Ifland Cryftal be pla- 
ced one after another, in fuch manner that all 
the Surfaces of the latter be parallel to all the 
correfponding Surfaces of the former: The 
Rays which are refradted after the ufual man- 
ner in the flrft Surface of the firft Cryftal, ftiall 
be reflated after the ufual manner in all the 
following Surliices j and the Rays which are re- 
fraded alter the unufual manner in the firft Sur- 
face, fhaii be relradted after the unufual manner 
in all tlie following Surfaces. And the fame thing 
happens, though the Surfaces of the Cryftals be 
any ways inclined to one another, provided that 
their Planes of perpendicular Refradlion be pa- 
rallel to ope another. 

And therefore there is an original difterencc 

an the Rays of Light, by means of which fome 

Rays are m this Experiment conftantly refra(S- 

k.' ed 



BOOK m. 333 

cd after the ufual manner, and others conftant- 
ly after the unufual manner : For if the diffe- 
rence be not original, but arifes from new Mo- 
difications imprefs'd on the Rays at their firft 
Refrad:ion, it would be aker'd by new Modi- 
fications in the three following Refractions; 
whereas it fuffers no alteration, but is conftant, 
and has the fame effed upon the Rays in all the 
Refractions. The unufual Refraction is there- 
fore perform'd by an original property of the 
Rays. And it remains to be enquired, whether 
the Rays have not more original Properties than 
are yet difcover'd. 

^. 26. Have not the Rays of Light feveral 
fides, endued with feveral original Properties ? 
For if the Planes of perpendicular Refradtion 
of the fecond Cryftal be at right Angles with 
the Planes of perpendicular RefraCtion of the 
firft Cryftal, the Rays which are refradted after 
the ufual manner in paffing through the firft 
Cryftal, will be all of them refradted after the 
unufual manner in pafling through the fecond 
Cryftal; and the Rays which are refradted af- 
ter the unufual manner in paffing through the 
firft Cryftal, will be all of them refradted after 
the ufual manner in paffing through the fecond 
Cryftal. And therefore there are not two forts 
of Rays differing in their nature from one ano- 
ther, one of which is conftantly and in all Po- 
fitions refradted after the ufual manner, and the 
other conftantly and in all Pofitions after the 
unufual manner. The difference between the 
two forts of Rays in the Experiment mention'd 
in the 25th Queftion, was only in the Pofitions 

I ©f 



334 O P T I C K S. 

of the Sides of the Rays to the Planes of pef<» 
pendicular Refrad:ion. For one and the fame 
Ray is here refraded fometimes after the ufual, 
and fometimes after the unufual manner, ac- 
cording to the Polition which its Sides have to 
the Cryflals. If the Sides of the Ray are poii- 
ted the fame way to both Cryflals, it is refra^ 
fted after the fame manner in them both : But 
if that fide of the Ray which looks towards 
the Coaft of the unufual Refradion of the iirft 
Cryftal, be 90 Degrees from that fide of the 
fame Ray which looks toward the Coaft of the 
unufual Refradion of the fecond Cryltal, (which 
may be effected by varying the Pofition of the 
fecond Cryftal to the firft, and by confequence 
to the Rays of Light, ) the Ray {hall be refraded 
after feveral manners in the feveral Cryflals. 
There is nothing more required to determine 
whether the Rays of Light which fall upon the 
fecond Cryflal fhall be refraded after the ufual 
or after the unufual manner, but to turn about 
this Cryflal, fo that the Coafl of this Cryflal's 
unufual Refradion may be orf this or on that 
fide of the Ray. And therefore every Ray may 
be confider'd as having four Sides or Quarters, 
two of which oppofite to one another incline 
the Ray to be refradled after the unufual man- 
ner, as often as either of them are turn'd to- 
wards the Coafl of unufuil Refradion j and the 
other two, whenever either of them are turn'd 
towards the Coafl of unufual Refradion, do not 
incline it to be otherwife refracted than after 
the ufual manner. The two iirfl may there- 
fore be call'd the Sides of unufual Refradion- 

And 



BOOK in. 335 

And fince thefe DifpofitioRS were in the Rays 
before their Incidence on the fecond, third, and 
fourth Surfaces of the two Cryflals, and fuffer- 
ed no alteration ( fo far as appears, ) by the Re- 
fra(flion of the Rays in their paflilge through 
thofe Surfaces, and the Rays v/ere refrad:ed by 
the fame Laws in all the four Surfaces ; it ap- 
pears that thofe Difpofitions were in the Rays 
originally, and fufier'd no alteration by the firil 
Refradion, and that by means of thofe Difpofi- 
tions the Rays -were refradied at their Incidence 
on the firft Surface of the firfh Cryilal, fome of 
them after the ufual, and fome of them after the 
unufual manner, accordingly as their Sides of 
vinufual Refradion were then turn'd towards the 
Coaft of the unufual Refradion of that Cryilal, 
or lideways from it. 

Every Ray of Light has therefore two oppo- 
fite Sides, originally endued with a Property on 
which the unufual Refradion depends, and the 
other two oppofite Sides not endued with that 
Property. And it remains to be enquired, whe- 
ther there are not more Properties of Light by 
which the Sides of the Rays differ, ani are di- 
ftinguifh'd from one another. 

In explaining the difference of the Sides of 
the Rays above mention'd, I have fuppofed that 
the Rays fall perpendicularly on the firfl Cry- 
ftal. But if they falK obliquely on it, the Suc- 
cefs is the fame. Thofe Rays which are refra- 
ded after the ufual manner in the firfl Cryflal, 
will be refraded after the unufual manner in the 
fecond Cryflal, fuppoiing the Planes of perpen- 
dicular 



336 O P T I C K a 

dicular Refradtion to be at right Angles with one 
another, as above j and on the contrary. 

If the Planes of the perpendicular Refraction 
of the two Cryflals be neither parallel nor per- 
pendicular to one another, but contain an acute 
Angle : The two beams of Light which emerge 
out of the firfl Cryftal, will be each of them di- 
vided into two more at their Incidence on the fe- 
cond Cryftal. For in this cafe the Rays in each 
of the two beams will fome of them have their . 
Sides of unufual Refradlion, and fome of them 
their other Sides turn'd towards the Coaft of the 
unufual Refradtion of the fecond Cryftal. 

^/. 27. Are not all Hypothefes erroneous 
which have hitherto been invented for explain- 
ing the Phaenomena of Light, by new Modifica- 
tions of the Rays ? For thofe Phaenomena de- 
pend not upon new Modifications, a§ has been 
fuppofed, but upon the original and unchange- 
able Properties of the Rays. 

^. 28. Are not all Hypothefes erroneous, 
in which Light is fuppofed to confift in Pref- 
lion or Motion, propagated through a fluid Me- 
dium ? For in all thefe Hypothefes the Phaeno- 
mena of Light have been hitherto explain'd by 
fuppofing that they arife from new Modifica- 
tions of the Rays j which is an erroneous Sup- 
pofition. 

If Light confifted only in PreiTion propaga- 
ted without adhial Motion, it would not be a- 
ble to agitate and heat the Bodies which refrad: 
and refledl it. If it confifted in Motion propa- 
gated to all diftances in an inftant, it would re- 
quire an infinite force every moment, in every 

fhining 



BOOK IIL 337 

fhinlng Particle, to generate that Motion. And 
if it confiiled in Preflion or Motion, propaga- 
ted either in an inftant or in time, it would bend 
into the Shadow.' For Preffion or Motion 
cannot be propagated in a Fluid in right Lines, 
beyond an Obitacle which ftops part of the Mo- 
tion, but will bend and fpread every way into 
the quiefcent Medium which lies beyond the 
Obftacle. Gravity tends downwards, but the 
PrelTure of Water arifnig from Gravity tends 
every way with equal Force, and is propagated 
as readily, and with as much force lideways as 
downwards, and through crooked paflages as 
through ftaait ones. The Waves on the Surface 
of ftagnating Water, paffing by the fides of a 
broad Obftacle which Itops part of them, bend 
afterwards and dilate themfelves gradually into 
the quiet Water behind the Obftacle. The 
Waves, Pulfes or Vibrations of the Air, where- 
in Sounds confift, bend manifeftly, though not 
fo much as the Waves of Water. For a Bell 
or a Cannon may be heard beyond a Hill which 
intercepts the fight of the founding Body, and 
Sounds are propagated as readily through crook- 
ed Pipes as through ftreight ones. But Light 
is never known to follow crooked Paftages nor 
to bend into the Shadow. For the fix'd Stars 
by the Interpofition of any of the Planets ceafe 
to be fien. And fo do the Parts of the Sun 
by the Interpofition of the Moon, Mercury or 
Venm. The Rays which pafs very near to the 
edges of any Body, are bent a little by the adion 
of the Body, as we ftiew'd above j but this 
bending is not towards but from the Shaiow, 

Z and 



338 O P T I C K S. 

and is perform'd only in the paffage of the Ray 
by the Body, and at a very fmall diftance from 
it* So foon as the Ray is pafl the Body, it goes 
right on. 

To explain the unufual Refra^ion of Ifland 
Cryftal by PreiTion or Motion propagated, has 
not hitherto been attempted ( to my knowledge) 
except by Huygms^ who for that end fuppofed 
two feveral vibrating Mediums within that Cry- 
ftal. But when he tried the Refradions in two 
fucceffive pieces of that Cryftal , and found 
them fuch as is mention'd above; he confef- 
fed himfelf at a lofs for explaining them. For 
PrefTions or Motions, propagated from a Ihining 
Body through an uniform Medium, muft be 
on all fides alike j whereas by thofe Experi- 
ments it appears, that the Rays of Light have 
different Properties in their different Sides. He 
fufpeded that the Pulfes of /Ether in pafling 
through the firft Cryftal might receive certain 
new Modifications, which might determine 
them to be propagated in this or that Medium 
within the fecond Cryftal, according to tht 

Pofition of that Cryftal. 
M^is tour dirt comment But what Modifications 

ceU fe fait, je nay rlen ^l^^fg might be he COuld 
trove jufqu id qui me fa- r. ^ i • i r 

tisfaje. c. H. de la iumi- Hot lay, nor think of any 
ere. c. 5. p. 91. thing fatisfadory in that 

Point. And if he had 
knov^n that the unufual Refradlion depends not 
on new Modifications, but on the original and 
unchangeable Difpofitionsof theRays, he would 
have found it as difficult to explain how thofe 
Pifpofitions which he fuppofed to be imprefs'd 

_ on 



BOOK IIL 339 

on the Rays by the firft Cryftal, could be in 
them before their Incidence on that Cryftal, 
and in general, how all Rays emitted by £hi- 
ning Bodies, can have thpfe Difpofitions in 
them from the beginning. To me , at leafl:, 
this feems inexplicable ,. if Light be nothing 
elfe than Preffion or Motion propagated through 
Mther, 

And it is as difficult to explain by thefe Hy- 
pothefes, how Rays can be alternately in Fits 
of eafy Reflexion and eafy Tranfmiffion j unlefs 
perhaps one might fuppofe that there are in all 
Space two ^Ethereal vibrating Mediums, and 
that the Vibrations of one of them conftitute 
Light, and the Vibrations of the other are fwift- 
er, and as often as they overtake the Vibrations 
of the firft, put them into thofe Fits. But how 
two Mthers can be diffufed through all Space, 
one of which ads upon the other, and by con- 
fequence is re-a<5led upon, without retarding, 
fliattering, difperling and confounding one an- 
others Motions, is inconceivable. And againft 
filling the Heavens with fluid Mediums, unlefs 
they be exceeding rare, a great Objedion arifes 
from the regular and very lafting Motions of 
the Planets and Comets in all manner of Courfes 
through the Heavens. For thence it is mani- 
feft, that the Heavens are void of all fenfible 
Refiftance, and by confequence of all fenfible 
Matter. 

For the refifling Power of fluid Mediums a- 
rifes partly from the Attrition of the Parts of 
the Medium, and partly from the Vis inertia 
of the Matter. That part of the Refiftance of 

Z 2 afphe- 



340 O P T I C K S. 

a fpherical Body which arifes from the Attrition 
of the Parts of the Medium is very nearly as the 
Diameter, or, at the moft, as the FaSfum of the 
Diameter, and the Velocity of the fpherical Bo- 
dy together. And that part of the Reliflance 
which arifes from the Vis inertia of the Matter, 
is as the Square of that FaBiim. And by this 
difference the two forts of Refiftance may be di- 
flinguifh'd from one another in any Medium; 
and thefe being diftinguifh'd, it will be found 
that almoft all the Refiftance of Bodies of a com- 
petent Magnitude moving-in Air, Water, Quick- 
filver, and fuch like Fluids with a competent Ve- 
locity, arifes from the Vis inertice of the Parts of 
the Fluid. 

Now that part of the refifting Power of any 
Medium which arifes from the Tenacity, Fri- 
ction or Attrition of the Parts of the Medium, 
may be dimini(h'd by dividing the Matter into 
fmaller Parts, and making the Parts more fmooth 
and flippery: But that part of the Refiftance 
which arifes from the Vis inerti(X, is proportio- 
nal to the Denfity of the Mattel, and cannot be 
diminifh'd by dividing the Matter into fmaller 
Parts, nor by any other means than by decrea- 
iing the Denlity of the Medium. And for thefe 
Reafons the Denlity of fluid Mediums is very 
nearly proportional to their Refiftance. Li- 
quors which differ not much in Denfity, as Wa- 
ter, Spirit of Wine, Spirit of Turpentine, hot 
Oil, differ not much in Refiftance. Water is 
thirteen or fourteen times lighter than Quick- 
. iilver, and by confequence thirteen or fourteen 
times rarer, and its Refiftance is lefs than that 

of 



BOOK III. 341 

of Quick-filver in the fame Proportion, or there- 
abouts, as I have found by Experiments made 
with Pendulums. The open Air in which we 
breathe is eight or nine hundred times lighter 
than Water, and by confequence eight or nine 
hundred times rarer, and accordingly its Refi- 
ftance is lefs than that of Water -in the fame 
Proportion, or thereabouts j as I have alfo found 
by Experiments made with Pendulums. And in 
thinner Air the Reiiftance is ftill lefs, and at 
length, by ratifying the Air, becomes infenfi- 
ble. For fmall Feathers falling in the open Air 
meet with great Refiftance, but in a tall Glafs 
well emptied of Air, they fall as fail as Lead or 
Gold, as I have feen tried feveral times. Whence 
the Refiftance feems ftill to decreafe in propor- 
tion to the Denlity of the Fluid. For I do not 
find by any Experiments, that Bodies moving 
in Quick-filver, Water or Air, meet with any 
oaher fenfible Refiftance than what arifes from 
the Denfity and Tenacity of thofe fenfible Flu- 
ids, as they would do if the Pores of thofe Flu- 
ids, and all other Spaces, were filled with a 
denfe and fubtile Fluid. Now if the Refiftance 
in a Veffel well emptied of Air, was but an 
hundred times lefs than in the open Air, it 
would be about a million of times lefs than in 
Quick- filver. But it feems to be much lefs in 
fuch a Veffel, and. ftill much lefs in the Hea- 
vens, at the height of three or four hundred 
Miles from the Earth, or above. For Mr. Boyle 
has fliew'd that Air may be rarified above ten 
thoufand times in VefTels of Glafs j and the 
Heavens are much emptier of Air than any Va-^ 

23. cuiim 



342 O P T I C K S. 

cuum we can make below. For fmce the Air 
is comprefs'd by the Weight of the incumbent 
Atmoiphere., and the Denfity of Air is propor- 
tional to the Force compreffing it, it follows by 
Computation, that at the lieight of about fe- 
ven and a half Engliflj Miles from the Earth, the 
Air is four times rra-er than at the Surface of the 
Earth J and at the height of 15 Miles it is fix- 
teen times rarer than that at the Surface of the 
Earth J and at the height of 22^, 30, or 38 Miles, 
it is refpedively 64, 256, or 1024 times rarer, 
or thereabouts J and at the height of 76, 152, 
228 Miles, it is about loooooo, 1 000000000000, 
or loooGOOoooooooooooo times rarer j and fo 
on. 

Heat promotes Fluidity very much, by dimi- 
nifliing the Tenacity of Bodies. It makes ma- 
ny Bodies fluid which are not fluid in cold, and 
increafes the Fluidity of tenacious Liquids, as 
of Oil, Balfam, and Honey, and thereby de- 
creafes their Refiftance. But it decreafes not 
the Refiftance of Water confiderably, as it would 
do if any confiderable part of the Refiftance of 
Water arofe from the Attrition or Tenacity of 
its Parts. And therefore the Refiftance of Wa- 
ter arifes principally and almoft entirely from 
the Vis inertice of its Matter j and by confe- 
quence, if the Heavens were as denfe as War» 
ter, they would not have much lefs Refiftance 
than Water J if as denfe as Quick-filver, they 
would not have much lefs Refiftance than Quicks 
filver; if abfolutely denfe, or full of Matter 
without any Vacimm^ let the Matter be never 
fo fubtil and fluid, they would have a greater 

Refiftance 



BOOK m. 343 

Refiftance than Qulck-filver. A folid Globe in 
fuch a Medium would lofe above half its Mo- 
tion in moving three times the length of its 
Diameter, and a Globe not folid ( fuch as are 
the Planets, ) would be retarded fooner. And 
therefore to make way for the regular and lad- 
ing Motions of the Planets and Comets,- it's ne- 
ceffary to empty the Pleavens of all Matter, ex% 
cept perhaps fome very thin Vapours, Steams, 
or Effluvia, arifmg from the Atmofpheres of the 
Earth, Planets, and Comets, and from fuch an 
exceedingly rare ;^thereal Medium as we de- 
fcribed above. A denfe Fluid can be of no ufe 
foi- explaining the Phaenomena of Nature, the 
Motions of the Planets and Comets being better 
explain'd without it. It ferves only to difturb 
and' retard the Motions of thofe great Bodies, 
and make the Frame of Nature languifh : And 
in the Pores of Bodies, it ferves only to ftop 
the vibrating Motions of their Parts, wherein 
their Heat and A<fl:ivity conlifts. And as it is 
of no ufe, and hinders the Operations of Na- 
ture, and makes her languifn, fo there is no e- 
vidence for its Exiftence, and therefore it oueht 
to be rejected. And if it be rejeded, the Hy- 
pothefes that Light confiils in Preffion or Mo- 
tion, propagated through fuch a Medium, are 
rejeded with it. 

And for rejeding fuch a Medium, we have 
the Authority of thofe the oldeft and moll ce- 
lebrated Philofophers -of Greece and Phcenkiay 
who made a Vacuum^ and Atoms, and the Gra- 
vity of Atoms, the firft Principles of their Phi- 
lofophyj tacitly attributing Gravity to fo.Ec- o- 

Z 4 thci 



344- O P T I C K S. 

ther Caufe than denfe Matter. Later Philofo- 
phers baniili the Confi deration of fuch a Caufe 
out of natural Philofophy, feigning Hypothefes 
for explaining all things mechanically, and re- 
ferring other Caufes to Metaphylicks : Whereas 
the main Bufniefs of natural Philofophy is to 
argue from Phcenomena without feigning Hy- 
pothefes, and to deduce Caufes from Effects, 
till we come to the very firft Caufe, which cer- 
tainly is not mechanical ; and not only to un- 
fold the Mechanifm of the World, but chiefly 
to refolve thefe and fuch like Queftions. What 
is there in places almofl empty of Matter, and 
whence is it that the Sun and Planets gravitate 
towards one another, without denfe Matter be- 
tween them ? Whence is it that Nature doth 
nothing in vain ; and whence arifes all that Or- 
der and Beauty which we fee in the World ? 
To what end are Comets, and whence is it that 
Planets move all one and the fame way in Orbs 
concentrick, while Comets move all manner of 
ways in Orbs very excentrick ; and what hinders 
the fix'd Stars from falling upon one another ? 
How came the Bodies of Animals to be contri- 
ved with fo much Art, and for what ends were 
their feveral Parts ? Was the Eye contrived 
without Skill in Opticks, and the Ear without 
Knowledge of Sounds ? Plow do the Motions 
of the Body follow from the Will, and whence 
is the Inftindt in Animals ? Is not the Senfory of 
Animals that place to which the fenfitive Sub- 
itance is prefent, and into which the fenfible 
Species of Things ap carried through jthe Nerves 
and Brain, that there they may be perceived 



BOOK III. 345 

by their immediate prefence to that Scbftancc ? 
And thefe things being rightly difpatch'd, does 
it not appear from Plia^nomena that there is a 
Being incorporeal, living, intelligent, omnipre- 
fent, who in infinite Space, as it were in his Sen- 
fory, fees the things themfelves intimately, and 
throughly perceives them, and comprehends 
them wholly by their immediate prefence to 
himfelf : Of which things the Images only car- 
ried through the Organs of Senfe into pur little 
Senforiums, are there feen and beheld by that 
which in us perceives and thinks. And though 
every true Step made in this Philofophy brings us 
not immediately to the Knowledge of the firll 
Caufe, yet it brings us nearer to it, and on that 
account is to be highly valued. 

^. 29. Are not the Rays of Light very 
fmall Bodies emitted from lliining Subllances ? 
For fuch Bodies will pafs through uniform Me- 
diums in right Lines without bending into the 
Shadow, which is the Nature of the Rays of 
Light. They will alfo be capable of feveral 
Properties, and be able to conferve their Pro- 
perties unchanged in paffing through feveral 
Mediums, which is another Condition of thq 
Rays of Light. Pellucid Subllauces a6t upon 
the Rays of Light at a diftance in refracting-, re- 
flecting, and inflecting them, and the Rays m.u- 
tually agitate the Parts of thofe Subfl:ances at ^a 
difl:arce for heating them i and this ACtion and 
Re-aUion at a difl:ance very much refembles an 
attractive Force between Bodies. If RefraCtion 
be perform'd by Attraction of the Rays, the 
Sines of Incidencs muft be to the Sines of Re- 
fraCtion 



346 O P T I C K S. 

fraftion in a given Proportion, as we {hew'd in 
our Principles of Philofophy : And this Rule is 
true by Experience. The Rays of Light in 
going out of Giafs into a Vacuum^ are bent to- 
wards the Glafs ; and if they fall too obliquely 
on the Vacuum^ they are bent backwards into 
the Glafs, and totally reflected j and ^ this Refle- 
xion cannot be afcribed to the Refiftance of an 
abfolute Vacuum^ but muft be caufed by the 
Power of the Glafs attracting the Rays at their 
going out of it into the Vacuum^ and bringing 
them back. For if the farther Surface of the 
Glafs be moiflen'd with Water or clear Oil, or 
liquid and clear Honey, the Rays which would 
otherwife be refleded will go into the Water, 
Oil, or Honey ; and therefore are not refle(5ted 
before they arrive at the farther Surface of the 
Glafs, and begin to go out of it. If they go out 
of it into the Water, Oil, or Honey, they 
go on, becaufe the Attraction of the Glafs is 
almoft balanced and rendered ineffectual by 
the contrary Attraction of the .Liquor. But if 
they go out of it into a Vacuum which has no 
Attraction to balance that of the Glals, the At- 
traction of the Glafs either bends and refraCts 
them, or brings them back and reflects them.- 
And this is ftill more evident by laying together 
two Prifms of Glafs, or two ObjeCt-glaSes of 
very long Telefcopes, the one plane, the o- 
ther a little convex, and fo compreffing them 
that they do not fully touch, nor are too far a- 
funder. For the Light which falls upon the 
farther Surface of the firfl Glafs where the In- 
terval between the Glaffes is not above the ten 

hundred 



BOOK III. 347 

hundred thoufandrh Part of an Inch, will go 
through that Surface, and through tbe Air or 
Vacuum between the GlaiTes, and enter into the 
fecondGlafs, as was explain'd in the firft, fourth, 
and eighth Obfervations of the firft Part of the 
fecond Book. But, if the fecond Glafs be taken 
away, the Light which goes out of the fecond 
Surface of the. firft Glafs into the Air or Va- 
cuum^ will not go on forwards, but turns back 
into the firft Glafs, and is reflecftcd ; and there- 
fore it is drawn back by the Power of the firft 
Glafs, there being nothing elfe to turn it back. 
Nothing more is requifite for producing all the 
variety of Colours, and degrees of Refrangibi- 
lity, than that the Rays of Light be Bodies of 
different Sizes, the leaft of which may take 
violet the weakeft and darkeft of the Colours, 
and be more cafily diverted by refrad:ing Sur- 
faces from the right Courfe ; and the reft as 
they are bigger and bigger, may make tlie 
ftronger and more lucid Colours, blue, green, 
yellow, and red, and be more and more diHi- 
cultly diverted. Nothing more is requifite for 
putting the Rays of Light into Fits of eafy Re- 
flexion and eafy Tranfmiffion, than that they be 
fmall Bocjies which by their attractive Powers, 
or fome other Force, ftir up Vibrations in what 
they ad; upon, which Vibrations being fwifter 
than the Rays, overtake them fucceftively, and 
agitate them fo as by turns to increafe and de- 
creafe their Velocities, and thereby put them 
into thofe Fits. And laftly, the unufual Refra- 
(ftion of Ifland-Cryftal looks very much as if it 
were perform'd by fome kind of attractive vir- 
tue 



348 O P T I C K S. 

tue lodged in certain Sides both of the Rays, 
and of the Particles of the Cryftal. For were 
it not for* fome kind of Difpofition or Virtue 
lodged in fome Sides of the Particles of the 
Cryflal, and not in their other Sides, and which 
inclines and bends the Rays towards the Coafl 
of unufual Refraction, the Rays which fall per- 
pendicularly on the Cryllal, would not be re- 
fraded towards that Coafl rather than towards 
any other Coaft, both at their Incidence and at 
their Emergence, fo as to emerge perpendicu- 
larly by a contrary Situation of the Coaft of 
unufual Refradion at the fecond Surface ; the 
Cryftal acting upon the Rays after they have 
■pafs'd through it, and are emerging into the 
Air; or, if you pieafe, into a V aciium' And 
lince the Cryftal by this Difpofition or Virtue 
does not ad: upon the Rays, unlefs when one 
of their Sides of unufual Refradion looks to- 
wards that Coaft, this argues a Virtue or Difpo- 
fition in thofe Sides of the Rays, which an- 
fwers to, and fympathizes with that Virtue or 
Difpofition of the Cryftal, as the Poles of two 
Magnets anfwer to one another. And as Mag- 
netifm may be intended and remitted, and is 
found only in the Magnet 2nd in Iron : So this 
Virtue of refrading the perpendicular Rays is 
greater in Ifland-Cryftal, lefs- in Cryftal of the 
Rock, and is not yet found in other Bodies. I 
do not fay that this Virtue is magnetical : It 
feems to be of another kind. I only fay, that 
wnatever it be, it's difficult to conceive how 
the Rays of Light, unlefs they be Bodies, can 
have a permanent Virtue in two of their Sides 
I which 



BOOK III. 349 

which is not in their other Sides, and this without 
any regard to their PoUtion to the Space or Me- 
dium through which they pafs. 

What I mean in this Queftion by a Vacuum^ 
and by the Attradions of the Rays of Light to- 
wards Giafs or Cryftal, may be undcrftood ' by 
what was faid in the i8th, 19th, and 20th Que- 
ftions. 

^eji. 30. Are not grofs Bodies and Light con- 
vertible into one another, and may not Bodies re- 
ceive much of their A(^l:ivity from the Particles 
of Light which enter their Compofition? For all 
fix'd Bodies being heated emit Light fo long as 
they continue fufficiently hot, and Light mutually 
flops in Bodies as often as its Rays ftrike upon 
their Parts, as we fliew'd above. I know no 
Body lefs apt to fliine than Water; and yet Wa- 
ter by frequent Diftillations changes into fix'd 
Earth, as Mr.Boy/e^ has try'd ; and then this Earth 
being enabled to endure a fufficient Heat, {hines 
by Heat like other Bodies. 

The changing of Bodies into Light, and Light 
into Bodies, is very conformable to the Courfe 
of Nature, which feems delighted with Tranf- 
mutations. Water, which is a very fluid taflelefs 
Salt, fhe changes by Heat into Vapour, which is 
a fort of Air, and by Cold into Ice, which is a 
hard, pellucid, brittle, fufible Stone ; and this 
Stone returns into Water by Heat, and Vapour 
returns into Water by Cold. Earth by Heat be- 
comes Fire, and by Cold returns into Earth. 
Denfe Bodies by Fermentation rarify into feve- 
ral forts of Air, and this Air by Fermentation, 
and fometimes without it, returns into denfe 

Bodies. 



350 O P T I C K S. 

Bodies. Mercury appears fometimes in the form 
of a fluid Metal, fometimes in the form of a hard 
brittle Metal, fometimes in the form of a corro- 
live pellucid Salt call'd Sublimate, fometimes in 
the form of a taftelefs, pellucid, volatile white 
Earth, call'd Mercip^ius Dulcis j or in that of a 
red opake volatile Earth, call'd Cinnaber j or in 
that of a red or vv^hite Precipitate, or in that of 
a fluid Salt ; and in Diftillation it turns into 
Vapour, and being .agitated i?i VaciiOj it fhines 
like Fire. And after all thefe Changes it re- 
turns again into its firfl: form of Mercury. 
Eggs grow from infenfible Magnitudes, and 
change into Animals j Tadpoles into Frogs ; 
and Worms into Flies. All Birds, Beaflis and 
Fifhes, Infers, Trees, and other Vegetables, 
with their feveral Parts, grow out of Water 
and watry Tinctures and Salts, and by Putre- 
fadtion return again into watry Subftances. And 
Water ftanding a few Days in the open Air, 
yields aTindurc, which (like that of Malt) by 
ftanding longer yields a Sediment and a Spi- 
rit, but before Putrefaction is fit Nourifhment 
for Animals and Vegetables. And among fuch 
various- and fl:range Tranfmutations, why may 
not Nature change Bodies into Light, and Light 
into Bodies ? 

^leji. 3 1. Have not the fmall Particles of Bo- 
dies certain Powers, Virtues, or Forces, by which 
they adt at a diftance, not only upon the Rays 
of Light for reflecting, refra(fling, and inflect- 
ing them, but alio upon one another for pro- 
ducing a great Part of the Phaenomena of Na- 
ture ? For it's well known, that Bodies ad: 

one 



BOOK TIL 351 

one upon anotlier by the Attradions of Gravity, 
Magnetifm, and Eledtricity j and thefe Inftances 
ihew the Tenor and Courfe of Nature, and make 
it not improbable but that there may be more at- 
tradlive Powers than thefe. For Nature is very 
confonant and conformable to her felf How 
thefe Attradtions may be perform'd, I do not here 
confider. What I call Attraction may be per- 
form'd by impulfe, or by fome other means un- 
known to me. I ufe that Word here to fignify 
only in general any Force by which Bodies tend 
towards one another, whatfoever be the Caufe. 
For we muft learn from the Phcenomena of 
Nature what Bodies attradt one another, and 
what are the Laws and Properties of the At- 
traction, before we enquire the Caufe by which 
the Attraction is perform'd. . The Attractions of 
Gravity, Magnetifm, and EleCtricity, reach to 
very fenfible diflances, and fo have been obferved 
by vulgar Eyes, and there may be others which 
reach to fo fmall diflances as hitherto efcape Ob- 
fervation j and perhaps eleCtrical Attraction may 
reach to fuch fmall diftances, even without being 
excited by FriCtion. 

For when Salt of Tartar runs per IDeliquium, 
is not this done by an Attraction between the 
Particles of the Salt of Tartar, and the Parti- 
cles of the Water which float in the Air in the 
form of Vapours ? And why does not common 
Salt, or Salt-petre, or Vitriol, run per Deliqimirn^ 
but for want of fuch an Attraction ? Or why 
docs not -Salt of Tartar drav^^ more Water out 
of the Air than in a certain Proportion to its 
quantity, but for want of an attractive Force 
2 after 



^52 O P T I C K S. 

after it is fatiated with Water ? And whence 
is it but from this attractive Power that Water 
which alone diftils with a gentle luke-warm 
Heat, will not diftil from Salt of Tartar with- 
out a great Heat ? And is it not from the like 
attractive Power between the Particles of Oil of 
Vitriol and the Particles of Water, that Oil of 
Vitriol draws to it a good quantity of Water 
out of the Air, and after it is fatiated draws no 
more, and in Diftillation lets go the Water very 
difficultly ? And when Water and Oil of Vi- 
triol poured fucceffively into the fame Veffel 
grow very hot in the mixing, does not this 
Heat argue a great Motion in the Parts of the 
Liquors ? And does not this Motion argue, that 
- the Parts of the two Liquors in mixing coa- 
lefce with Violence, and by confequence rufli to- 
wards one another with an accelerated Mo- 
tion ? And when Aqua fortis, or Spirit of Vi- 
triol poured upon Filings of Iron, dilTolves the 
Filings with a great Heat and Ebullition, is not 
this Heat and Ebullition effected by a violent 
Motion of the Parts, and does' not that Motion 
argue that the acid Parts of the Liquor rufh to- 
wards the Parts of the Metal with violence, 
and run forcibly into its Pores till they get be- 
tween its outmoft Particles, and the main Mafs 
of the Metal, and furrounding thofe Particles 
loofen them from the main Mafs, and fet them 
at liberty to float off into the Water ? And 
when the acid Particles, which alone would 
diftil with an eafy Heat, will not feparate from 
the Particles of the Metal without a very vio- 
lent 



BOOK III. 353 

lent Heat, does not this confirm the Attradtioa 
between them ? 

When Spirit of Vitriol poured upon com- 
mon Salt or Salt-petre makes, an Ebulhtion with 
the Salt, and unites wich it, and in Diftillatian ' 
the Spirit of the common Salt 'or Salt-petre 
comes over much eafier than it would do be- 
fore, and the acid part of the Spirit of Vitriol 
ilays behind j does not this argue that the fi:<'d 
Alcaly of the Salt attrads the acid Spirit ot the 
Vitriol more ftrongly than its own Spirit, and 
not being able to hold them both, lets go its 
own? And when Oil of Vitriol is draw^n off 
from its weight of Nitre j and from both the 
Ingredients a compound Spirit of Nitre is diflil- 
led, and two parts of this Spirit are poured on 
one part of Oil of Cloves or Carraway Seeds, or. of 
any ponderous Oil of vegetable or animal Sub- 
ftanCes, or Oil of Turpentine thicken'd with a 
little Balfam of Sulphur, and the Liquors grow fo 
very hot in mixing, as prefently to fend up a burn- 
ing Flame ; does not this very great and fudden 
Heat argue that the two Liquors mix with vio- 
lence, and that their Parts in mixing run to- 
wards one another with an accelerated Motion, 
and cla(h with the greateft Force ? And is it 
not for the fame reafon that well redlified Spi- 
rit of Wine poured on the fame compound Spi- 
rit fla{hes*f and that the Piilvis fuUninam, com- 
pofed of Sulphur, Nitre, and Salt of Tartar, 
goes off with a more fudden and violent Ex- 
plofion than Gun-powder, the acid Spirits of 
the Sulphur and Nitre ruihing towards one an- 
other, and towards the Salt of Tartar, with fo 

A a great 



354- O P T I C K S. 

great a violence, as by the (hock to turn the 
whole at once into Vapour and Flame ? Where 
the DilTolution is flow, it makes a flow Ebulli- 
tion and a gentle Heat j and where it is quick- 
er:, it makes a greater Ebullition with more 
heat ; and where it is done at once, the Ebul- 
lition is contraded into a fudden Blaft or vio- 
lent Explofion, with a heat equal to that of 
Fire and Flame. So when a Drachm of the a- 
bove-mention'd compound Spirit of Nitre was 
poured upon half a Drachm of Oil of Carraway 
Seeds i?i vaciio^ the Mixture immediately made 
a flafh like Gun-powder, and burll the ex- 
haufted Receiver, which was a Glafs fix Inches 
wide, and eight Inches deep. And even the 
grofs Body of Sulphur powder'd, and with an 
equal weight of Iron Filings and a little Water 
made into Pafte, ads upon the Iron,* and in five 
or fix hours grows too hot to be touch'd, and 
emits a Flame, And by thefe Experiments com- 
pared with the great quantity of Sulphur with 
which the Earth abounds, and the warmth of 
the interior Parts of the Earth, and hot Springs, 
and burning Mountains, and with Damps, mi- 
neral Corufcations, Earthquakes, hot fuffoca- 
ting Exhalations, Flurricanes, and Spouts; we 
may learn, that fulphureous Steams abound in 
the Bowels of the Earth and ferment with Mi- 
nerals, and fomietim^es take fire with a fudden 
Corufcatlon and Explofion; and if pent up in 
fubterraneous Caverns, burfl the Caverns with a 
great {baking of the Earth, as in fpringing of a 
Mine. And then the Vapour generated by the 
Explofion, expiring through the Fores of the 

3 Earth, 



BOOK III. 355 

Earth, feels hot and fuffocateSj and iiiakes Tem-« 
pefls and Hurricanes, and fometimes caufes the" 
Land to Hide, or the Sea to boil, and carries 
up the Water thereof in Drop3, which by their 
weight fall down again in Spouts, ^xlfo fome 
fulphureous Steams, at all times when the Earth 
is dry, afcending into the Air, ferment there 
with nitrous Acids^ and fometimes taking fire 
caufe Lightning and Thunder, and fiery Me- 
teors. For the Air abounds with acid Vapours 
fit to promote Fermentations, as appears by the- 
rufling of Iron and Copper in it, the kindling 
of Fire by blowing, and the beating of the 
Heart by means of Refpiration. Now the a- 
bove-mention'd Motions are fo great and violent 
as to fhew t]iat in Fermentations the Particles of 
Bodies which almofi: reft, are put into new Mo- 
tions by a very potent Principle, w^hich ad:s up- 
on them only when they approach one another, 
and caufes them to meet and clafh with 2;reat vi* 
olence, and grow hot with the motion, and dafli 
one another into pieces, and vapifli into Air, and 
Vapour, and Flame. 

When Salt of Tartar per deliqiiium^ being 
poured into the Solution of any Metal, preci- 
pitates the Metal, and makes it fail down to the 
bottom of the Liquor in the form of Mud: 
Does not this argue tliat the acid Particles are 
attracted more ftrong-ly by the Salt of Tartar 
than by the Metal, and by the ftronger Attra- 
d:ion go from the Metal to the Salt of Tartar ? 
And fo when a Solution of Iron in Anna forth 
diffolves the Lapis Calciminarh^ and lets go the 
Iron, or a Solution of Copper difiblves Iron im- 

A a 2 merfed 



356 O P T I C K S. 

irierfed in it and lets go the Copper, or a So- 
'4ution of Silver difTolves Copper and lets go the 
Silver, or a Solution of Mercury in Aquafortis 
being poured upon Iron, Copper, Tin, or Lead, 
difTolves the Metal and lets go the Mercury ; 
does not this argue that the acid Particles of 
the Aqua fortis are attracted more ftrongly by 
the Lapis Calamniaris than by Iron, and more 
flrongly by Iron than by Copper, and more 
ftrongly by Copper than by Silver j and more 
ftrongly by Iron, Copper, Tin, and Lead, than 
by Mercury ? And is it not for the fame reafon 
that Iron requires more Aqua fortis to dilTolve 
it than Copper, and Copper more than the other 
Metals ; and that of all Metals, Iron is dilTolved 
moft eafily, and is mofi: apt to ruft ; and next af- 
ter Iron, Copper? 

When Oil of Vitriol is mix'd w^ith a little 
Water, or is run per deliquiuni^ and in Diftil- 
lation the Water afcends difficultly, and brings 
over v^rith it fome part of the Oil of Vitriol in 
the form of Spirit of Vitriol, and this Spirit be- 
ing poured upon Iron, Copper,' or Salt of Tar- 
tar, unites with the Body and lets go the Wa- 
ter 'j doth not this fliew that the acid Spirit is at- ■ 
traded by the Water, and more attracted by 
the fix'd Body than by the Water, and there- 
fore lets go the Water to clofe v^ith the fix'd 
Body ? And is it not for the fame reafon that 
the Water and acid Spirits which are mix'd to- 
gether in Vinegar, Aqua fortis^ and Spirit of 
Salt, cohere and rife together in Diftillation ; 
but if the Mejiftruum be poured on Salt of Tar- 
tar, or on Lead, or Iron, or any fix'd Body 

which 



BOOK III. 357 

which it can diflblve, the Acid by a fironger At- 
traction adheres to the Body, and lets go ths 
Water ? And is it not alfo from a mutual At- 
tracftion that the Spirits o£ Soot and Sea-Sak 
unite and compofe the Panicles of Sal-armo- 
niac, which are lefs volatile than before, be- 
caufe grofler and frc€r from Water ; and that 
the Particles of Sal-armoniac in Sublimation car- 
ry up the Particles of Antimony, which will not 
fublime alone ; and that the Particles of Mer- 
cury uniting with the acid Particles of Spirit 
of Salt compofe Mercury fublimate, and with 
the Particles of Sulphur, compofe Cinnaber; 
and that the Particles of Spirit of Wine and 
Spirit of Urine well redlitied unite, and letting 
go the Water which dillblved them, compofe a 
confident Body; and that in fubliming Cinna- 
ber from Salt of Tartar, or from quick Lime, 
the Sulphur by a ftronger Attraftion of the Salt 
or Lime lets go the Mercury, and flays with 
the fix'd Body ; and that when Mercury fubli- 
mate is fublimed from Antimony, or from Re- 
gulus of Antimony, the Spirit of Salt lets go the 
Mercury, and unites with the antimonial Me- 
tal which attracts it more ftrongly, and ftays 
with it till the Heat be great enough to make 
them both afcend together, 'and then carries 
up the Metal with it in the form of a very fu^ 
fible Salt, called Butter of Antimony, although 
the Spirit of Salt alone be almoft as volatile as 
Water, and the Antimony alone as fix'd as 
Lead ? 

When yi^ua fortis diffolves Silver and not 
Gold, and Aqua regia diffolves Gold and not 

A a 3 Silver, 



35^ 



O P T I C K S. 



Silver, may it not be faid that Aqua forth is 
fubtil enough to penetrate Gold as well as Sil- 
ver, but wants the attracflive Force to give it 
Entrance j and that Aqua regia is fubtil enough 
to penetrate Silver as v/ell as Gold, but wants 
the attractive Force to give it Entrance ? For 
Aqua rcgia is nothing elfe than Aqua fortis 
mix'd v/ith fome Spirit of Salt, or with Sal-ar- 
moniac J and even common Salt diiTolved in A-^ 
qua fcrtis^ en.ibies the Metijiruwrn to dilfolve 
Gold, though the Salt be a grofs Body. When 
therefore Spirit of Snlt precipitates Silver out 
of Aqua fortis^ is it not done by attrading and 
jnixing with the Aqua Jortisy and not attrad:- 
jng, or perhaps repelling Silver? And when 
Water precipitates Antimony out of the Subli- 
mate of Antimony and Sal-armoniac, or out of 
putter of Antimony, is it not done by its dif^ 
folving, mixing with, and weakening the Sal^ 
grmoniac or Spirit of Salt, and its not attract- 
ing, or perhaps repelling the Antimony ? And 
is it not for want of an attradive virtue be- 
tween the Parts of Water and Oil, of Quick-^ 
lilver and Antimony, of Lead and Iron, that 
thefe Subllances do not mixj .and by a weak 
Attradion, that Quick-filver and Copper mix 
difiicultly j and fi'om a flrong one, that Quick- 
filver. and Tin, Antimony and Iron, Water and 
Salts, mix readily? And in general, is it not 
from the fame Principle that Heat congregates; 
homogeneal Bodies, and feparates heterogeneal 
ones? 

When Arfenick with Soap gives a Regulus^ 

and with Mercury fublimate a volatile fufible 

^ ■ Salt, 



BOOK III. 359 

Salt, like Butter of. Antimony, doth not this 
lliew that Arfenick, which is a Subftance totally 
volatile, is compounded of fix'd and volatile 
Parts, ftrongly cohering by a mutual Attradion, 
fo that the volatile will not afcend without car- 
rying up the fixed ? And fo, when an equal 
weight of Spirit of Wine and Oil of Vitriol 
are digefted together, and in Diftillation yield 
two fragrant and volatile Spirits which will not 
mix with one another, and a fix'd black Earth 
remains behind ; doth not this fliew that Oil of 
Vitriol is compofed of volatile and fix'd Parts 
ftrongly united by Attradion, fo as to afcend to- 
gether in form of a volatile, acid, fluid Salt, 
until the Spirit of Wine attrads and feparates 
the volatile Parts from the fixed ? And there- 
fore, fince Oil of Sulphur per Campcmam is of 
the fame Nature with Oil of Vitriol, may it not 
be inferred, that Sulphur is alfo a mixture of 
volatile and fix'd Parts fo ftrongly cohering by 
Attradion, as to afcend together in Sublima- 
tion. By diflblving Flowers of Sulphur in Oil 
of Turpentine, and diftilling the Solution, it is 
found that Sulphur is compofed of an inflama- 
ble thick Oil or fat Bitumen, an acid Salt, a 
very fix'd Earth, and a little Metal. The three 
firfl were found not much unequal to one 
another, the fourth in fo fmall a quantity as 
fcarce to be worth confidering. The acid Salt 
difix)lved in Water, is the fame with Oil of Sul- 
phur per Campanam, arid abounding .much in 
the Bowels of the Earth, and particularly in 
Markafites, unites it felf to the other Ingredi- 
ents of the Markafite, which are. Bitumen, I- 

A a 4 ron, 



360 O P T I C K S. 

ron. Copper, and Earth, acid with them corn- 
pounds Alkim, Vitriol, and Sulphur. With the 
Earth alone it compounds AUum ; with the Me- 
tal alone, or Metal and Earth together, it com- 
pounds Vitriol; and with the Bitumen and Earth 
it compounds Sulphur. Whence it comes to 
pafs that Markances abound v/ith thofe three Mi- 
nerals. And is it not from the mutual Attradtior^ 
of the Ingredients that they ftick together for 
ccmpoundins; thefe Minerals, and that the Bitu- 
men carries up the other Ingredients of the Sul- 
phur, which without it would not fublime ? And 
the fame Queftion may be* put concerning all, 
or almofc all the grofs Bodies in Nature. For 
all the Parts of Animals and Vegetables are com- 
pofed of Subftances volatile and fix'd, fluid and 
folid, as appears by their Analyfis ; and fo 
are Salts and Minerals, fo far as Chymifls have 
been hitherto abl? to examine their Compofi- 
tion. 

When Mercury fublimate is re-fublimed with 
frefh Mercury, and becomes Mercurius Dulcis^ 
which is a white taftelefs Earth fcarce dilTolva- 
ble in Water, and Mercurius Dulcis re-fublimed 
with Spirit of Salt returns into Mercury fubli- 
mate ; and when Metals corrpded with a little 
acid turn into ruft, which is an Earth taftelefs 
and indiffolvable in Water, and this Earth im- 
bibed with more acid becomes • a metallick 
Salt ; and when fome Stones, as Spar of Lead, 
diifolv^d in proper M^nfiruums become Salts ; 
do not thef.:; tilings fhew that Salts are dry Earth 
and watry Acid united by Attradion, and that 
the Earth \\all not become a Salt without fq 

muql^ 



BOOK III. 361 

much acid as makes it diffolvable in Water ? Do 
not the {harp and pungent Taftes of Acids 
arife from the ftrong Attradtion whereby the 
acid Particles rufli upon and agitate the Par- 
ticles of the Tongue ? And when Metals are dif- 
folved in acid MenJi?'immSy and the Acids in 
conjunction with the Metal ad after a different 
manner, fo that the Compound has a different 
Tafte much milder than before, and fometimes 
a fweet one j is it not becaufe the Acids ad-, 
here to the metallick Particles, and thereby 
lofe much of their Aftivity ? And if the Acid 
be in too fmall a Proportion to make the Com- 
pound diffolvable in Water, will it not by ad- 
hering flrongly to the Metal become unadive and 
lofe its Tafle, and the Compound be a taflelefs 
Earth ? For fuch things as are not diffolvable by 
the Moiflure of the Tongue, ad not upon the 
Tafle. 

As Gravity makes the Sea flow round the 
deafer and weightier Parts of the Globe of the 
Earth, fo the Attraction may make the watry 
Acid flow round the denfer and compader Par- 
ticles of Earth for compofing the Particles of 
Salt. For otherwife the Acid would not do 
the Ofhce of a Medium between the Earth and 
common Water, for making Salts diffolvable in 
the Water j nor would Salt of Tartar readily 
draw off the Acid from diffolved Metals, nor 
Metals the Acid from Mercury. Now, as in the 
great Globe of the Earth and Sea, the denfefl 
Bodies by their Gravity fink down in Water, 
^nd always endeavour to go towards the Cen- 
ter of the 'Globe; fo in Particles of Salt, the 

denfefl 



362 O P T I C K S. 

denfcft Matter may always endeavour to approach 
the Center of the Particle : So that a Particle of 
Salt may be compared to a Chaos ; being denfe, 
hard, diy, and earthy in the Center j and rare, 
foft, moift, and watry -in the Circumference. 
And hence it feems to be that Salts are of a 
lafting Nature, bejng fcarce dellroy'd, unlefs by 
drawing away their watry Parts by violence, 
or by letting them foak into the Pores of the 
central Earth by a gentle Heat in Putrefa- 
ction, until the Earth be diflblved by the Wa- 
ter, and feparated into fmaller Particles, which 
by reafon of their Smallnefs make the rotten 
Compound appear of a black Colour. Hence 
ilfo It may be, that the Parts of Animals and 
"Vegetables preferve their feveral Forms, and 
affimilate their Nouriihment j the foft and moift 
Nourifhment eafily changing its Texture by a 
gentle Heat and Motion, till it becomes like the 
denfe, hard, dry, and durable Earth in the Cen- 
ter of each Particle. But when the Nourilh- 
ment grows unfit to be allimilated, or the cen- 
tral Earth grows too feeble to affimilate it, the 
Motion ends in Confufion, Putrefacftion, and 
Death. 

If a very fmall quantity of any Salt or Vitriol 
be dilfolved in a great quantity of Water, the. 
particles of the Salt or Vitriol will not fmk to 
the bottom, though they be heavier in Specie 
than the Water, but will eveidy diffufe them- 
felves into all the Water, fo as to make it as fa- 
line at the top as at the bottom. And does not 
this imply that the Parts of the Salt or Vitriol 
recede from one another, and endeavour to ex- 
pand 



BOOK III. 363 

pand themfelves, and get as far afunder as the 
quantity of Water in which they float, will al- 
low ? And does not this Endeavour imply that 
they have a repulfive Force by which they fly 
from one another, or at leaft, that they attrad: 
the Water more llrongly than they do one ano- 
ther ? For as all things afcend in Water which 
are lefs attraded than Water, by the gravitating 
Power of the Earth j fo all the Particles of Salt 
which float in Water, and are lefs attraded than 
Water by any one Particle of Salt, muil recede 
from that Particle, and give way to the more at- 
traded V/ater. 

When any faline Liquor is evaporated to aCu- 
ticle and let cool, the Salt concretes in regular 
Figures j which argues, that the Particles of the 
Salt before they concreted, floated in the Liquor 
^t equal difl:ances in rank and file, and by confe- 
quence that they aded upon one another by fome 
Power which at equal diilances is equal, at une- 
qual diftances unequal. For by fuch a Power 
they will range themfelves uniformly, and with- 
out it they will float irregularly, and come to- 
gether as irregularly. And fmce the Particles 
of Ifland-Cryftal ad all the fame way upon 
the Rays of Light for caufing the unufual Re- 
fradion, may it not be fuppofed that in the For- 
mation of this Cryfl:al, the Particles not only 
ranged themfelves in rank and file for concreting 
in regular Figures, but alfo by fome kind of po- 
lar Virtue turned their homogeneal Sides the 
fame way. 

The Parts of all homogeneal hard Bodies 
which fully touch one another, flick together 

N'ery 



364 OPTIC K S. 

very ftrongly. And for explaining how this 
may be, fome have invented hooked Atoms, 
which is begging the Queftion^ and others tell 
us that Bodies are glued together by reft, that 
is, by an occult Quf.lity, or rather by nothing; 
and others, that they flick together by confpi- 
ring Motions, that is, by relative reft . amongft 
themfelves. I had rather infer from their Co- 
hefion, that their Particles attrad: one another by 
fbme Force , which in immediate Contaft is ex- 
ceeding ftrong, at fmall diftances performs the 
chymical Operations above-mention'd , and 
reaches not far from the Particles with any fenfi- 
ble -Effea. 

All Bodies fcem to be compofed of hard Par- 
ticles : For otherwife Fluids would not congeal 5 
as Water, Oils, Vinegar , and Spirit or Oil of 
Vitriol do by freezing ; Mercury by Fumes of 
Lead; Spirit of Nitre and Mercury, by diflbl- 
ving the Mercury and evaporating the Flegm ; 
Spirit of Wine and Spirit of Urine, by deflegm- 
ing and mixing them; and Spirit of Urine and 
Spirit of Salt, by fubliming them together to 
make Sal-armoniac. Even the Rays of Light 
feem to be hard Bodies ; for otherwife they 
would not retain different Properties in their 
different Sides, And therefore Hardnefs may 
be reckon'd the Property of all uncompounded 
Matter. At leaft, this feems to be as evident 
as the univerfal Impenetrability of Matter. For 
all Bodies, fo far as Experience reaches, are ei- 
ther hard, or may be harden'd; and we have 
no other Evidence of univerfal Impenetrability, 
befides a large Experience without an experi- 
mental 



BOOK III. 365 

mental Exception. Now if compound Bodies 
are fo very hard as we find fome of them to 
be, and yet are very porous, and confift of Parts 
which are only laid together j the fimple Par- 
ticles which are void of Pores, and were never 
yet divided, muft be much harder. For fuch 
hard Particles being heaped up together, can 
fcarce touch one another in more than a few 
Points, and therefore muft be feparable %by 
much lefs Force than is requifite to break a fo~ 
lid Particle, whofe Parts touch in all the Space 
between them, without any Pores or Interftices 
to weaken their Cohelion. And how fuch ve- 
ry hard Particles which are only laid together 
and touch only .in a few Points, can flick toge- 
ther, and that (b firmly as they do, without the 
a{rifi;ance of fomething which caufes them to 
be attracted or prefs'd towards one another, is 
very difficult to conceive. 

The fame thing I infer alfo from the cohe- 
ring of two polifh'd Marbles in vacuo^ and from 
tlie llanding of Quick-filver in the Barometer at 
the height of 50, 60 or 70 Inches, or above, 
when ever it is well-purged of Air and careful- 
ly poured in, fo that its Parts be every where 
contiguous both to one another and to the 
Glais. The Atmofphere by its weight prefles 
the Quick-filver into the Glafs, to the height of 
29 or 30 Inches. And fome other Agent railes 
it higher, not by preihng it into the Glafs, but 
by making its Parts flick to the Glafs, and to 
one another. For upon any difcontinuation of 
Parts, made either by Bubbles or by fhaking the 

Glafs, 



366 O P T I C K S. 

Glafs, the whole Mercury falls down to the 
height of 29 or 30 Inches. 

And of the fame kind with thefe Experi- 
ments are thofe that follow. If two plane po- 
lifh'd Plates of Glafs ( fuppofe two pieces of a 
polifh'd Looking-glafs ) be laid together, fo that 
their fides be parallel and at a very fmall di- 
ftance from one another, and then their lower 
edggs be dipped into Water, the Water will 
rife up between them. And the lei's the di- 
ftance of the Glaffes is, the greater will be the 
height to which the Water will rife. If the 
diftance be about the hundredth part of an Inch, 
the Water will rife to the height of about an 
Inch J and if the diilance be greater or lefs in 
any Proportion, the height will be reciprocally 
proportional to the diftance very nearly. For 
the attractive Force of the Glaffes is the fame, 
whether the diftance between them be greater 
or lefsi and the weight of tlie Water drawn 
up is the fame, if the height of it be recipro- 
cally proportional to the diftance of the Glaffes. 
And in like manner , Water afcends between 
two Marbles polifti'd plane, when their poliftied 
lides are parallel, and at a very little diftance 
from one another. And if flender Pipes of 
Glafs be dipped at one end into ftagnating Wa- 
ter, the Water will rife up within the Pipe, and 
the height to which it riles will be reciprocally 
proportional to the Diameter of the Cavity of 
the Pipe, and will equal the height to which it 
rifes between two Planes of Glafs, if the Semir- 
diameter of the Cavity of the Pipe be equal to 
the diftance betv/een the Planes, or thereabouts. 

And 



BOOK IIL 367 

An.d thefe Experiments fucceed after the fame 
manner in 'vacuo as in the open Air, (as hath 
been tried before the Royal Society, ) and there- 
fore are not influenced by the Weight or Pref- 
fiire of t!^e Atmofphere. 

And if a large Pipe of Giafs be fiiied with 
fifted Afhes well preffed together in the Glafs, 
.and one end of the Pipe be dipped into ftagna- 
ting Water, the Water will rife up flowly^ in 
the Afhes, fo as in the fpace of a Week or Fort- 
night to reach up within the Glafs, to the height 
of 30 or 40 Inches above the ftagnating Water. 
And the Water rifes up to this height by the 
Action only of thofc Particles of the Aihes which 
are upon the Surface of the elevated Water; 
the Particles which are within the Water, at- 
tra6ting or repelling it as much downwards as 
upwards. And therefore the Action of the Par- 
ticles is very ftrong. But the Particles of the 
Alhes being not lb denfe and clofe together 
as rhofe of Glafs, their Action is not fo flrong 
as that of Glafs, which keeps Quick- fiiver fuf- 
pended to the height of 60 or 70 Inches, and 
therefore a6ls with a Force which would keep 
Water fufpcnded to the height of above 60 
Feet. 

By the fame Principle, a Sponge fucks in 
Water, and the Glands in the Bodies of Ani- 
mals, according to their feveral Natures and 
Difpofitions, fuck in various Juices from the 
Blood. . ■ - 

If two plane polifh'd Plates of Gafs three or 
four Inches broad, and twenty or twenty five 
long, be laid one of them parallel to the Ho- 
rizon, 



368 O P T I C K S. 

1-izon, the other upon the firft, fo as at one of 
their ends to touch one another, and contain an 
Angle of about lo or 15 Minutes, and the fame 
be firft moiften'd on their inward fides with a 
Glean Cloth dipp'd into Oil of Oranges or Spirit 
of Turpentine, and a Drop or two of the Oil 
or Spirit be let fall upon the lower Glafs at thei. 
other end j fo foon as the upper Glafs is laid • 
down upon the lower, fo as to touch it at one 
end as above, and to touch the Drop at the other 
end, making with the lower Glafs an Angle of 
about 10 or 15 Minutes; the Drop will begin to 
move towards the Concourfe of the GlalTes, and 
will continue to move with an accelerated Mo- 
tion, till it arrives at that Concourfe of the 
Glailes. For the two Glaffes attradt the Drop, 
and make it run that way towards which the At-^ 
tradlions . incline. And if when the Drop is in 
motion you lift up that end of the Glaffes where 
they meet, and towards which the Drop moves, 
the Drop will afcend between the Glaffes, and 
therefore is attracted. And as you lift up the 
Glaffes more and more, the Drop will afcend 
flower and flower, and at length reit, being then 
carried downward by its Weight, as much as up- 
wards by the Attraction. And by this means 
you may know the Force by which the Drop is 
attracted at all diftances from the Concourfe of 
the Glaffes. ^ 

Now by fome Experiments of this kind, 
(made by Mr. Hauksbee) it has been found that 
the Attraction is almofl reciprocally in a dupli- 
cate Proportion of the diflance of the middle 
of the Drop from the Concourfe of the Glaffes, 

viz. 



BOOK III. 369 

1/2;. reciprocally in a limple Propoition, by rea- 
fon of the fpreading of the Drop, and its touch- 
ing each Glafs in a larger Surface; and again re- 
ciprocally in a fimple Proportion, by* reaibn of 
the Attradions growing ftronger within the 
fame quantity of attracting Surface. The At- 
traction therefore within the fame quantity of 
attrading Surface, is reciprocally as the diftance 
between the Glaiies. And therefore where the 
diftance is exceeding fmall, the Attraction muft 
be exceeding great. By the Table in the fe- 
cond Part of the fecond Book, wherein the 
thicknefles of colour'd Plates of Water be- 
tween two Glafles are fet down, the thicknefs 
of the Plate where it appears very black, is 
three eighths of the ten hundred thoufandth 
part of an Inch. And where the Oil of O- 
ranges between the Glafles is of this thicknefs, 
the Attraction coUeCled by the foregoing Rule, 
feems to be fo ftrong, as within a Circle of an 
Inch in diam.eter, to fuffice to hold up a 
Weight equal to that of a Cylinder of Water 
of an Inch in diameter, and two or three Fur- 
longs in length. And where it is of a lefs 
thicknefs the Attraction mny be proportionally 
greater, and continue to increafe, until the 
thicknefs do not* exceed that of a iinglc Par- 
ticle of the Oil. There are therefore Agents 
in Nature able to make the Particles of Bo- 
dies ftick together by very ftrong Attractions. 
And it is the Bufinefs o£ experimental Philofophy 
to find them out. 

B b ^ . Now 



370 O P T I C K S. 

fjow the fmalleft Particles of Matter may co- 
here by the ftrongeil Attra61:ions, and compofe 
bigger Particles of weaker Virtue ; and many of 
thele may* cohere and compofe bigger Particles 
whofe Virtue is flill weaker, and fo on for divers 
Succeffions, until the Progrellion end in the big- 
geft Particles on which the Operations in Chymi- 
Itry, and the Colours of natural Bodies depend, 
and which by cohering compofe Bodies of a fen- 
fible Magnitude. If the Body is compact, and 
bends or yields inward to Preflion without any 
Hiding of its Parts, it is hard and elaftick, re- 
turning to 'its Figure with a Force riling from 
the mutual AttracCtion of its Parts. If the 
Parts flide upon one another, the Body is mal- 
leable or foft. If they flip eafily, and are of a 
fit Size to be agitated by Heat, and the Heat is 
big enough to keep them in Agitation, the Body 
is fluid ; and if it be apt to flick to things, it is 
humid ; and the Drops of every fluid affed a 
round Figure by the mutual Attradiion of their 
Parts, as the Globe of the Earth and Sea affedrs a 
round Figure by the mutual Attraction of its Parts 
by Gravity, 

Since Metals difTolved in Acids attradt but a 
fniall quantity of the Acid, their attradiive Force 
can reach but to a fmall diftance from them. 
And as in Algebra, where affirmative Quanti- 
ties vanifli and ceafe, there negative ones be- 
gin J fo in Mechanicks, where Attradion cea- 
fes, there a repulfive Virtue ought to fucceed. 
And that there is fuch a Virtue, feems to fol- 
low from the Reflexions and Inticxions of the 
I Rays 



BOOK III. 371 

Rays of Light. For the Rays are repelled by 
Bodies in both thefe Cafes, without the imme- 
diate Contad; of the reflecting or inflecting Bo- 
dy. It feems alfo to follow from the Emillion 
of Light ; the Ray fo foon as it is ihaken off 
from a fhining Body by the vibrating Motion of 
the Parts of the Body, and gets beyond the 
reach of Attraction, being driven away with ex- 
ceeding great Velocity. For that Force which 
is fufficient to turn it back in Reflexion, may 
be fufficient to emit it. It feems alfo to fol- 
low from the Produdion of Air and Vapour. 
The Particles when they are fjjaken off from 
Bodies by Heat or Fermentation, fo foon as 
they are beyond the reach of the Attradion of 
the Body, receding from it, and alfo from one 
another with great Strength, and keeping at a 
diftance, fo as fometimcs to take up above a 
Million of Times more fpace than they did be- 
fore in the form of a denfe Body. WliicJi vafh 
Contradion and Expanfion feems unintelligible, 
by feigning the Particles of Air to be fpringy 
and ramous, or rolled up like Hoops, or by 
any other means than a repulfive Power. The 
Particles of Fluids which do not cohere 100 
ftrongly, and are of fuch a Smallncfs as renders 
them mofl: fufceptibk of thofe Agitations which 
keep Liquors \n a Fluor, are mofl: eafily fepa- 
rated and rarifled into Vapour, and in the Lan- 
guage of the Chymifl:s, they are volatile, rari- 
fying with an eafy Heat, and condenfing with 
Cold. But thofe which are groffer, and fo lefs 
ibfceptible of Agitationj or cohere by a flironger 
B b 2 Attradion, 



372 O P T I C K S. 

Attradlon, are not feparated without 'a fironger 
Pleat, or perhaps not without Fermentation. 
And thefe iaft are the Bodies which Chymifls 
call fix'd, and being rarified by Fermentation, 
become true permanent Air j thofe Particles re- 
ceding from one another with the greateft 
Force, and being moft difficultly brought toge- 
ther, which upon Conrad: cohere moft ftrongly. 
And becaufe the Particles of permanent Air are 
grofter, and arife from denfer Subftances than 
thofe of Vapours, thence it is that true Air is 
more ponderous than Vapour, and that a moift 
Atmofphere is lighter than a dry one, quantity 
for quantity. From the fame repelling Power 
it feems to be that Flies walk, upon the Wa- 
ter -without wetting their Feet ; and that the 
Obje<5t-giaiTes of long Telefcopes lie upon one 
another without touching j and that dry Pow- 
ders are difficultly made to touch one ano- 
ther fo as to ftick together, unlefs by melting 
them, or wetting them with Water, which by 
exhaling may bring them together ; and that 
two poliih'd Marbles, which by immediate Con- 
tad ftick together, are difficultly brought fo 
clofe together as to ftick. 

And thus Nature will be very conformable 
to herfelf and very fimple, performing all the 
great Motions of the heavenly Bodies by the 
Attradion of Gravity which intercedes thofe 
Bodies, and almoft^U the fmall ones of their 
Particles by fome other attractive and repelling 
Powers which intercede the Particles. The 
Vis inertias is a paffive Principle by which Bo- 
dies 



BOOK III. 373 

dies perfift in their Motion or Reft, receive Mo- 
tion in proportion to the Force kiiprefTing it, 
and refift as much as they are itfifted. By 
this Principle alone there never could Ivxvq been 
any Motion in the World. Some other Principle 
was neceffary for putting Bodies into Motion ; 
and now they are in Motion, fome other Prin- 
ciple is neceflary for conferving the Motion. 
For from the various Compofition of two Mo- 
tions, 'tis very certain that there is not always 
the fame quantity of Motion in the World. For 
if two Globes joined by a Ilendtr Rod, revolve 
• about their common Center of Gravity with 
an uniform Motion, while that Center moves 
on uniformly in a right Line drawn in the 
Plane of their circular Motion j the Sum of 
the Motions of the two Globes, as often as the 
Globes are in the right Line defcribed by their 
common Center of Gravity, will be bigger than 
the Sum of their Motions, when they are in a 
Line perpendicular to that right Line. By this 
Liftance it appears that Motion may be got or 
loft. But by reafon of the Tenacity of Fluids, 
and Attrition of their Parts, and the Weakneli 
of Elafticity in Solids, Motion is much more 
apt to be loft than got, and is always -upon the 
Decay. For Bodies which are either abfolutely 
hard, or fo foft as to be void of Elafticity, 
will not rebound from one another. Impene- 
trability makes them only ftop. If two equal 
Bodies meet diredly t^i 'vacuo, they will by the 
Laws of Motion ftop where they meet, and 
lofe all their Motion, and remain in reft, unlefs 

B b 3 they 



374 O P T I C K S. 

they be elafcick, and receive new Motion froi^ 
their Spring. If they have lb much Elafticit] 
aSifuffices to make them re- bound with a quar- 
ter, or half, or three quarters of tlie Force with 
which they come together, they will lofe three 
quarters, or half, or a quarter of their Motion. 
And this may be try'd, by letting two equal 
Pendulums fall againft one another from equal 
heights. If the Pendulums be of Lead or foft 
Clay, they will lofe all or almoft all tlieir Mo- 
tions: If of elaftick Bodies they will lofe all but 
what they recover from their Elafticity. If it 
be faid, that they can lofe no Motion but what . 
they communicate to other Bodies, the confe- 
quence l;, that i?t vacuo they can lofe no Mo- 
tion, but when they meet they muft go on and 
penetrate one another's Dimenlions. If three 
equal round Veffels be filled, the one with Wa- 
ter, the other with Oil, the third with molten 
Pitch, and the Liquors be ftirred about alike 
to give them a vortical Motion j the Pitch by 
its Tenacity will lofe its Motion quickly, the 
Oil being lefs tenacious will keep i^ longer, and 
the Water being lefs tenacious will keep it long- 
eft, but yet will lofe it in a fliort time. Whence 
it is eafy to underftand, that if many contiguous 
Vortices of molten Pitch were each of them as 
large as thofe which fome fuppofe to revolve 
about the Sun and fix'd Stars, yet thefe and all 
their Parts would, by their Tenacity and Stiffnefs, 
communicate their Motion to one another till 
they all refted among themfelves. Vortices of 
Oil or Water, or fome fluider Matter, might 

continue 



BOOK III. 375 

continue longer in Motion ; but unlefs the Mat- 
ter were void of all Tenacity and Attrition of 
Parts, and Communication of Motion, (which 
is not to be fuppofed,) the Motion v/ould con- 
ftantly decay. Seeing therefore the variety of 
Motion which we find in the World is ahvays 
decreafing, there is a neceflity of confer ving 
and recruiting it by adive Principles, fuch as 
are the caufe of Gravity, by which Planets and 
Comets keep their Motions in their Orbs, and 
Bodies acquire great Motion in falling; ai>d the 
caufe of Fermentation, by which the Heart and 
Blood of Animals are kept in perpetual Motion 
and Heat; the inward Parts of the Earth are 
conftantly warm'd, and in fome places grow 
very hot; Bodies burn and fhine. Mountain^ 
take Fire, the Caverns of the Earth are blown 
up, and the Sun continues violently hot and 
lucid, and warms all things by his Light. For 
we meet with very little Motion in the World, 
befides what is owing to thefe ad:ive Principles. 
And if it were not for thefe Principles, the Bo- 
dies of the Earth, Planets, Comets, Sun, and 
all things in them, would grow cold and freeze, 
and become inadtive Mafles ; and all Putrefadi- 
on, Generation, Vegetation and Life would ceafe, 
and the Planets and Comets would not remain in 
their Orbs. 

All thefe things being confider'd, it feems pro- 
bable to me, that God in the Beginning form'd 
Matter in folid, mafly, hard, impenetrable, move- 
able Particles, of fuch Sizes and Figures, and with 
fuch other Properties, and in fuch Proportion 

B b 4 to 



376 OPTIC K S. 

to Space, as moft conduced to the End £o\ 
which he form'd them j and that thefe primi-) 
tive Particles being Solids, are incomparably 
harder than any porous Bodies compounded of 
them J even lb very hard, as never to v^^ear or 
break in pieces ; no ordinary Pov^er being able 
to divide what God himfelf made one in the jErft 
Creation. While the Particles continue entire, 
they may compofe Bodies of one and the fame 
Nature and Texture in all Ages : But fhould 
they wear away, or break in pieces, the Nature 
of Things depending on them, would be chan- 
ged. Water and Earth, compofed of old worn 
Particles and Fragments of Particles, would not 
be of the fame Nature and Texture now, with 
Water and Earth compofed of entire Particles 
in the Beginning. And therefore, that Nature 
may be lafting, the Changes of corporeal Things 
are to be placed only in the various Separations 
and new Aflbciations and Motions of thefe per- 
manent Particles j compound Bjodies being apt 
to break, not in the midfi of fclid Particles, but 
where thofe Particles are laid together, and only 
touch in a few Points. 

It feems to me farther, that thefe Particles 
have not only a Vis i?ierticej accompanied with 
fuch paffive Laws of Motion as naturally refult 
from that Force, but alfo that they are moved 
by certain adive Principles, fuch as is that of 
Gravity, and that which caufes Fermentation, 
and the Cohefion of Bodies. Thefe Principles 
I confider, not as occult Qualities, fuppofed to 
refult from the fpeciiick Forms of Things, but 

as 



BOOK in. 377 

PS general Laws of Nature, by which the Things 
themfelves are form'd; their Truth appearing 
to us by Phenomena, though their Caufes be 
not yet difcover'd. For theie are manifeil Qua- 
lities, and their Caufes only are occult. iVud 
the Arijloteiians gave the Name of occult Qua- 
lities, not to manifeil Qualities, but to iuch 
Qualities only as they fuppofed to lie hid im 
Bodies, and to be the unknown Caufes of ma- 
nifeft Effeds : Such as would be the Caufes of 
Gravity, and of m.agnetick and eledrick At- 
tradtions, and of Fermentations, if we fliould 
fuppofe that thefe Forces or Adions arofc from 
Qucilities unknov/n to us, and uncapable of be- 
ing difcovered and made manifeil. Such oc- 
cult Qualities put a Hop to the Improvement 
of natural Philofophy, and therefore of. late 
Years have been rcjedled. To tell us that e-r 
very Species of Thii^gs is endow'd with an oc- 
cult fpecifick Quality by which it ads and pro- v 
duces manifefl Etfeds, is to tell us nothing: But 
to derive two or three general Principles of Mo- 
tion from Phaenomena, and afterwards to tell us 
how the Properues and Adions of ail corporeal 
Things follow from thofe manifeil Principles, 
would be a very great ilep in Philofophy, though 
the Caufes of thofe Principles were not yet dif- 
cover'd : And therefore I fcruple not to propbfe 
the Principles of Motion above-mention'd, they 
being of very general Extent, and leave tl^ir* 
Caufes to be found out. 

Now by the help of thefe Principles, all ma- 
terial Things feern to have been comoofed of 

the 



378 O P T I C'k S. 

the hard and folid Particles above-mention'! 
varioufly aiTociated in the iirfl Creation By th) 
Counfel of an intelligent Agent. For it beeame) 
him who created them to fet them in order. 
And if he did fo, it's unphilofophical to feek 
for any other Origin of the World, or to pre- 
tend that it might arife out of a Chaos by the 
mere Laws of Nature j though being once 
form'd, it may continue by thofe Laws for ma- 
ny Ages. For while Comets move in very ex- 
centrick Orbs in all manner of Pofitions, blind 
Fate could never make all the Planets move 
one and the fame way in Orbs concentrick, 
fome inconfiderable Irregularities excepted, 
which may have rifen from the mutual Ad:ions 
of Comets and Planets upon one another, and 
which will be apt to increafe, till this Syflem 
wants a Reformation. Such a wonderful Uni- 
formity in the Planetary Syflem mufl be allow- 
ed the Effect of Choice. And fo muft the 
Uniformity in the Bodies of Animals, they ha- 
ving generally a right and a left fide fhaped a- 
like, and on either fide of theii: Bodies two 
Legs behind, and either two • Arms, or two 
Legs, or two Wings before upon their Shoul- 
ders, and between their Shoulders a Neck run- 
ning down into a Back-bone, and a Head up- 
on it J and in the Head two Ears, two Eyes, a 
Nofe, a Mouth, and a Tongue, alike fituated. 
•Alfo the firfl Contrivance of thofe very artifi- 
cial Parts of Animals, the Eyes, Ears, Brain, 
Mufcles, Heart, Lungs, Midriff, Glands, La- 
rynx, Hands, Wings, fwimming Bladders, na- 
tural 



BOOK III. 379 

. nral Spedlacles, and other Organs of Senfe and 
Motion J and the Inftin(!^ of Brutes and Infeds, 
can be the effed of nothing elfe than the Wif- 
dom and Skill of a powerful ever-living Agent, 
who being in all Places, is more able by 
his Will to niove the Bodies within his bound- 
lefs uniform Senforium, and thereby to form 
and reform the Parts of the Univerfe, than we 
are by our Will to move the Parts of our own 
Bodies. And yet we are not to confider the 
World as the Body of God, or the feveral Parts 
thereof, as tlie Parts of God. He is an uni- 
form Being, void of Organs, Members or Parts, 
and they are his Creatures fubordinate to him, 
and fubiervient to his Will j and he is no more 
the Soul of them, than the Soul of Man is the 
Soul of the Species of Things carried through 
the Organs of Senfe into the place of its Sen- 
fation, where it perceives them by means of its 
immediate Prefence, without the Intervention 
of any third thing. The Organs of Scnic are 
not for enabling the Soul to perceive the Spe- 
cies of Things in its Senforium, but only for 
conveying them thither j and God has no need 
of fuch Organs, he being every where prefent 
to the Things themfelves. And fince Space is 
divifible in injimtum^ and Matter is not necef- 
farily in all places, it may be, alfo allow'd that 
God is able to create Particles of Matter of fe- 
veral Sizes and Figures, and in feveral Propor- 
. tions to Space, and perhaps of different Denli- 
ties and Forces, and theieby to vary the Laws 
of Nature, and make Worlds of feveral forts in 

feveral 



380 O P T I C K S. 

feveral Parts of the Univerfe. At leafl, I fee i^j- 
thiiig of Contradidiion in all this. 

As in Mathematicks, fo in Natural Philofo- 
phy, the Inveftigation of difficult Things by the\ 
Method of Analyfis, ought ever to precede the 
Method of Compofition. This Analylis con- 
fifts in making Experiments and Obfervations, 
and in drawing general Concluiions from them 
by Induction, and admitting of no Objections 
againft the Conclufions, but fuch as are taken 
from Experiments , or other certain Truths. 
For Hypothefes are not to be regarded in ex- 
perimental Philofophy. And although the ar- 
guing from Experiments and Obfervations by 
Induction be no Demonftration of general Con- 
clufions ; yet it is the befl way of arguing which 
the Nature of Things admits of, and may be 
looked upon as fo much the flronger, by how 
much the Induction is more general. And if 
no Exception occur from Phaenomena, the Con- 
clufion may be pronounced generally. But if 
at any time afterwards any Exception fliall oc- 
cur from Experiments, it may then begin to be 
pronounced with fuch Exceptions as occur. By 
this way of Analylis we may proceed from Com- 
pounds to Ingredients, and from Motions to the 
Forces producing them j and in general, from 
Effeds to their Caufes , and from particular 
Cauies to more general ones, till the Argument 
end in the moll general. This is the Method 
of Analyfis : And the Synthefis coniifls in af- 
fuming the Caufes difcover'd, and eftablifh'd 
as Principles, and by them explaining the Phae- 

nomena 



{ BOO K III. 381 

noraena proceeding from them, and proving the 
Explanations." 

In the two firfl -Books of thefe Opticks, I 
. proceeded by this Analyfis to difcover and prove 
' the original Differences of the Rays of Light in 
refped: of Refrangibility, Reflexibility, and Co- 
lour, and their alternate Fits of eafy Reflexion 
and eafy Tranfmiffion, and the Properties of 
Bodies, both opake and pellucid, on which 
their Reflexions and Colours depend. And 
thefe Difcoveries being proved, may be alTumed 
in the Method of Compofition for explaining 
the Phzenomena arifmg from them: An In- 
ftance of which Method I gave in the End of 
the firft Book. In this third Book I have only 
begun the Analyfis of what remains to be dif- 
cover'd about Light and its Eflfcdts upon the 
Frame of Nature, hinting feveral things about 
it, and leaving the Hints to be examin'd and 
improv'd by the farther Experiments and Ob- 
fervations of fuch as are inquifitive. And if 
natural Philofophy in all its Parts, by purfuing 
this Method, Ihall at length be perfedied, the 
Bounds of Moral Philofophy will be alfo enlar- 
ged. For fo far as we can know by natural 
Philofophy what is the firlt Caufe, what Power 
he has over us, and what Benefits we receive 
from him, fo far our Duty towards him, as well 
as that towards one another, will appear to us 
by the Light of Nature. And no doubt, if the 
Worlhip of falfe Gods had not blinded the Hea*- 
then, their moral Pmioibphy would have gone 
farther than to the four Cardinal Virtues j and 

infi:ead 



382 



O P T I C K S. 



infteadof teaching the Tranfmigration of Souls, 
and to worfhip the Sun and Moon, and dead 
Heroes, they would have tajught us to worfhip 
our true Author and Benefactor, as their Ance- 
ftors did under the Government of Noah and his 
Sons before they corrupted themfelves. 



FINIS. 




BOOKS printed for William Innys. 

Is A A CI Newtoni, Equ. Aur. in Academia Cantabrigienfi Ma- 
thefeos olim Profeflbris Lucafiani Leftiones opiicae. 4/0. 1729. 

The fame in Englijh. %vo. 1728. 

Univerfal Arithmctick. By Sir Ifaac Newton. The Second E- 
dition. %vo. 1728. 

Opticas : Sive de Reflexionibus, Refraflionibus, Inflexionibus & 
Coloribus Lucis Libri ties, Authore Ifaaco Newton, Equite Au- 
rato. Latine reddidit Samuel Clarke, S. T. P. Editio fecunda, 
auftior. 8cff. 1719- 

Philofophise Naturalis Principia Mathcmatica. Authore Ifaaco 
Newton, Equ. Aur. Editio tertia, aufta ^ emendata. \to. 1726. 

The Method of Fluxions both Direft and Inverfe : The former 
being a Tranllation from the Marquis de V Hofpital, and the latter 
fupplied by the Tranflator, E. Stone, F. R. S. Jn two Volumes. 
%vo. 1730. _ / 

Epiilola ad amicum de Cotelii Inventis Ciirvarum ratione, ^V. 
\to. 1722. 

An Analytick Treatife of Conic Sedlions. By E. Stone. \t9. 

Mathematical Elements of Natural Phiiofophy confirm'd by Ex- 
periments : Or an Introduftion to Sir Ij'aac Newton's Phiiofophy. 
By1V.J.'sGravefandt,hL.D. In two Vols. 8:/^. The Third 
Edition. 1726. 

Phyfico-Theology : Or a Demonftration of the Being and Attri- 
butes of God, from his Works of Creation ; with large Notes and 
many curious Obfervations. By IV. Derham, Canon of WindjoTy 
and F. R. S. The Seventh Edition. %vo. 1727. 

Mr. Derhani's Allro-ThcoJogy : Or a Demonftration of the Be- 
ing and Attributes of Gc I from a Survey of the Heavens; with 
Cuts. The Fifth Edition. Sr-a. 1726. 

Philofophical Letters between the la:e Learned Mr. Ray and fe- 
veral of his Ingenipus Correfpendents, Natives and Foreigners. To 
which are added thofe of fra^icis Wiiloughby, Efq; The whole 
confining of many curious Difcoverics and Improvements in the 
Hii^ory of Quadrupeds, Birds, Fifr.es, Infefts, Plants, Fofiils, 
Fountains, idc. Publifhed by Mr. Dcrhatn. Zvo. 

Mr. Ray\ Three Phyiico-Theologlcal Difcourfes, concerning 
I. The primitive Chaos, and Creation of the World. II. The 
general Deluge, its Caufes artd EfFedls. III. The DilTolution of 
the World and future Conflagration, l^c. Illuftrated with Copper- 
Plates. The fourth Edition, with Additions. %vo. 

His Wifdom of God in the Works of the Creation. The 

Ninth Edition. %vo. 1727. 

Mr. Ronayne\ Treatile of Algebra. The Second Edition, with 
Additions. Sec. 1727 

Geometria Organica : Sive Defcriptio Linearum Curvarum uni- 
verfilis. Auftore Colino Mac Laurin, Math. Col. Abred. Prof. & 
R. S. S. 4/(?. 1720. 

Aa 



BOOKS printed for W. I n N y s. • 

An Introduftion to Natural Philofophy : Or PhiJorophrcal Le- 
£lures read in the Univerfity of Oxford, A. D. 1 700. To which 
zre added, The DcmonHrations of Mr. Huyge?;is Theorems, con- 
cerning Force and circular Motion. By yo/:?n Kei'/, M. D. Sav. 
Prof, of Allronomy, and F. R. S. The Second Edition. Svff. 

PhilofophicrJ Tranfaclinns, giving fome Account of the prefent 
"Ehidertakings, Studies and Labours of the Ingenious, in many con- 
fiderable Parts of the World. Vol. 36. Continued and publifh'd 
by JV. Rr/ity, M. D. and Reg. Soc. Seer. 4/1?. 1730. 

The Lives of the French, Italian and Gerjnaii Philofophers, late 
Members of the Royal Academy of Sciences in Paris. Together 
with Abftracls of the chqicefl Pieces communicated by them to that 
Tlluftrious Society. To which is added, the Preface of the Ingeni- 
ous Monfieur Fonicnelie, Sccretgry and Author of the Hiilory of 
the faid x'\cademy, ^vo. 

\Leonaidi Plukeneti'. M. D. Opera omnia Botanica in fex Tomoe 
divifa,. viz. I. II. III. Phytographise. IV. Almageftum Botani- 
<wm. V. Almagefti Botanici MantifTa. VI. Amaltheum Botani- 
cum in quibus Stirpes illuftriores minus cognitae, exoticae, Rarioref- 
due novjffime detcftae ad plures Chiliadas defcribuntur. Turn 
ionibus Tabulis JEntis CCCCLIV. fumma cura depiftis Figu- 
fintur. 

I Methodus Incrementorum direfla & univerfa. Auftore Brook 
Taylor, L. L. D. & Reg. Soc. Seer. 4/^. 171 7. 
i The Pollhumous Works of Dr. Robert Hcoke; in which, I. The 
j^refcnt Deficiency of natural Philofophy is difcourfed of, with 
tiie Methods of rendring it more certain and beneficial. II. Of 
the Nature, Motion and Effedls of Light, particularly that of the 
Sun and Comets. III. An hypothetical Explication of Memory ; 
how the Organs made ufe of by the Mind in its Operation may be 
inechanically underftood. IV. An Hypothefis and Explication of 
^e Cauie of Gravity, or Gravitation, Maignetifm, iffc. V. Dif- 
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fcveral : To which are annex'd, Phyfical Explicntions of feveral 
of the Fables in Oviifs Metamorphofis, very difisrent from other 
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runt nunc demum cafus nonnulli oppido rari. Authorc J. Allen, M.D. 
Editio tertia;, prioribus, triente plus, auftior. In 2 Vol. 'ivo. 1729. 



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